Introduction to MATLAB

1. Introduction: Hello everyone and welcome to Introduction to MATLAB course. This is engineered, done and I will be your guide through this course. Matlab, as a word stands for Matrix Laboratory. However, it as a program, it is a programming language developed by Mathworks. Started out as a matrix programming language where linear algebra programming was simple. It can be at on both under interactive sessions and as a batch job. This tutorial, it gives you a aggressively agenda introduction of MATLAB programming language. It is designed to give students fluency in MATLAB programming language. Problem-based MATLAB examples have been given in simple and easy way to make your learning fast and effective. As if do requisite, you have to check your computer specifications first, your computer should have a graphic God, greater than OpenGL 3.3 and minimum processor of X86 dash 64. In case you don't know these specifications from your laptop, you can just go to PC details and you will see your graphic card and your processor where you can compare their addition with the OpenGL three points three, and know whether MATLAB is downloadable at your computer. Now you can go to the MATLAB software downloaded and also have a license for short as a prerequisite, you need 90 minutes of the time, because this course needs no more than 90 minutes to be learned as an introduction for you to be able to run MATLAB as the beginning of the audience. This tutorial has been prepared for the beginners to have them understand basic to advanced functionality of MATLAB. After completing this tutorial, you will find yourself at a moderate level of expertise and using MATLAB from where you can take yourself to the next 11th. This is really essential. This course was designed in order to give you the main basics. Where do you will be able to investigate in each topic of MATLAB and study it all by yourself. This is really essential because you can see dividend MATLAB courses that are narrowed to a certain topic. This course gives you the basics of everybody think in MATLAB and gives you the skill of understanding how MATLAB thinks and work accordingly. Why learning MATLAB? Matlab allows you to implement and test your algorithms internally developed the computational codes also easily debug, easily use a large database of guilt and algorithms, but assess still images and creeds, simulation videos easily. So I'm going to make it simply a simple quotation. Matlab is simply the best. And always at each update is getting better. It makes your life easier. As someone who needs MATLAB, this course is really essential for you. Additional advantages of MATLAB is symbolic. Symbolic computation can be easily done. Call external libraries, again, import any other library needs related to different areas of MATLAB before extensive data analysis and visualization, such as simply stating that you will learn inserting any equation and it will plot your graph developed application with the graphics user interface. As an agenda, we will use MATLAB as a calculator. We will write, we learn how to override the variable appearance of floating point numbers managing the workday. So you again know what are the main sections of Matlab, where to go in case I need help, in case I'm searching for a certain command where I can find this command and during multiple statements, also mathematical functions, basic plotting which I previously talked about the visualization, matrix generation at a properties and solving linear equation with MATLAB, you will learn how to solve linear equation over 68910, the non-bird you want or variables not being limited to the it that limits you to three or four variables only. As a contact, I am putting in your hands, my email, my phone number, and my LinkedIn account in case you face any problem through the course, in case you have any question through the project that I inserted at the end of the course, you can just contact me at anytime. I'm ready to help. I wish you enjoy this course and wish you the best of luck. Thank you. 2. MATLAB AS CALCULATOR: Hello everyone, Welcome to MATLAB as a calculator. Matlab, as we know, is Matrix Laboratory. However, this doesn't mean that it is not a calculated. It cannot compute and run basic arithmetic commands such as plus, minus times and division and a lot more. So let's prove this by just starting to plus three, for example, just keeping the two plus three without any semi-colons or any columns, just keeping it as a formula with nothing. And running this section, the MATLAB understands that I'm just trying to run something without writing a true script. So I'm just using it as a calculator. So two plus three is very simple. It gives me five as an answer. Now, five minus two and run this section, we got three. So the plus is similar to the calculator and the plus, the minus is also similar. However, when it comes to the multiplication, we use this star symbol, so two times three and run this section, we got six. So we reflect the multiplication of two numbers with the star symbol. Now, what about the division? The division is simple by the right division slash, the right slash, and we run it, excuse me, I'm running it as a script. Run this section, I get 0.667. So this is the main arithmetic operations of a calculator, the plus, minus multiplication and the division. However, matlab also considers the hierarchy of operations or the preference. In case I'm pressing one plus two times three, I get one plus two times three. So one, it stops. Plus two times three, it has a greater preference. The multiplication and the division have higher preferences in the hierarchy of operations over the addition, the plus, he enters two plus two times three equals six. Then plus one, I get a seven. This is not the case. If, if I haven't the hierarchy of operations, then I have one plus two is 33 times three equals nine. However, it will show me the seventh. So I have the hierarchy of operations. It's not dumped. It's a true calculator. It has all arithmetic rules and procedures. Let's take it to another level. What about 13 times two minus three plus four divided by two? So we previously know that the multiplication start first from the left. It goes to the division. So 13 plus two, I got it 26, then four divided by two, I get a 226 minus three. I get it 23 plus two, I get it one-to-five. Let's run this section. I got it. However, there is something that over or dominate own preferences is the parenthesis. If I insert any parenthesis in my operation, what is inside my paranthesis or the main or the first operations to build on. So times two minus three plus four. Matlab will start directly inside the parenthesis. Two minus three, minus one plus four equals three. So he starts by inside the parenthesis. Then he runs the normal arithmetic operations from left to the right. Let's run this section. I get 19.5. That's everything about MATLAB as the calculator. Let's move on to overwriting a variable and start with the beginner phases of MATLAB. 3. Overwriting a variable: Now starting with overwriting evaluated, writing a variable, Let's start with finding, let's say D, B in the lowercase, deep equal five. Then ending this slide with a semicolon for MATLAB to understand that I finished t equal five only. I'm not displaying t equals five in case I kept it like this, it will form at t equal five. However, just d equal five semicolon. Stopping this, I'm overwriting a variable. Matlab understands that in case I had a valuable and I want to change it if I am able to do so in case I did, dv equals six. Now, running this section, I won't have to equal five. I would have to equal six because in the work space of MATLAB, d equals 5. Second line, the following line, teeth with sex, it overwriting. There is a professional way to overwrite, used as an increment in for loops. This is a little bit advanced in programming, so I would just give it as an idea. I won't use it in this class. However, just keep it in mind. D equal, which means five plus one. This refers that deep equal five plus one equals six. So between Give me the same answer, d equals six. By this, we've finished OCO writing about it. It's a small section. It's not advanced, just giving you an idea in case you were trying to write the script and you are stuck to override the body. But just don't panic. Use the increment function t equal t plus one. And the problem is solved. 4. APPEARANCE OF FLOATING POINT NUMBER: That MATLAB in the same value of the same variable, the same input, everything, the same gun, show it in different formats because floating point numbers or variables can be, for example, 1.3353. How many numbers after the comma or after the point I should include, I have 24 months, the format short and the format long. We can use it simply. However, in the advanced sections, when we will use the parent and the percentage of, we will use another technique in order to control the number of commas after a float point number. Let's start by defining a float number x equal minus 163.667. That's everything to know. What should I include? I have two formats, the format short and the format long. Let's keep it in the format short, then press X. Let's run this section. I get just minus 163.667 zeros added is 0. Even if it is short, he is programmed in a way that the short format includes four numbers after the point. The, This is everything in the short section. I can't control using the formats anymore. However, in case I pressed it as format long and I run this section, I get minus 1.636670 e plus 0. This is a scientific calculation using a format long. In this case, it is just three points after the variable. If you want, I can change it 7894 and then run this section. I got it in short format. In the long format and the short format, I got it as just four points or four numbers after the point with rounding the final one. So 667, the third, the fourth seven, is followed by a number above five. So it rounds upwards to minus 163.6678. This is when it comes to appearance of floating-point number. Let's move on to managing the workplace in order to understand where to work and how to manage working on market. 5. Managing the workplace: Arriving to the managing of the work place session. Now I'm just showing you what are the main features of MATLAB in terms of visual where you can work where and you got the answer, etc.. Let's start with the basic. Here in the home, you can create a new script. You can create a live script where a programmers or engineers mainly, if they are working on a group project and they are working together, so they just save it on an online cloud where they can adjust, adjust and have a permission to edit, etc. You can create different sections system, object, project figures, applications, even. You can open a file or similar file that was already registered on your computer. You can import data. This is the workspace where we have the main variables and here you can create a new variable. However, without just pressing this button, you can just say X equals five. Here I created a new variable, so this is not very useful. However, you can conducted in certain programming issues and you can use also an open variable when it comes to coding. This is a little bit advanced and we will not interpret that now. And the Simulink is also advanced. When you give an equation that runs over a period of time, MATLAB is able to conduct this equation and chose and ends up with a graph or that a final result that shows how this variable is changing with time corresponding to other variables. When it comes to the environment and the resources, you can just ask help. If you have the license for MATLAB, you can learn MATLAB from a resources that MATLAB group has suggested. Also, you can request a support and certain definition and certain commands. You are not comfortable. You are not succeeding with something. You can just ask MATLAB about the main technical problem. And also we have a community that access MathWorks online community. This is when it comes to home. The Blots are another section where I will and interpret it. So in the second level of this class, after three or four sections, we will start plotting some graphs. And here you can see that we can change the area, we can turn it into a board or scatter or a pie histogram. We have different types, a lot of MATLAB types that we can use when it comes to the apps. Also, we have different apps that are integrated using MATLAB. If you have a good and you are studying numerical analysis, this is a little bit advanced in math. You just use the code fitting and it will generate a fit for the good according to different studies. So you can choose a optimization be idea. Junior This is oriented to some mathematical operations, not in our case. Just learn how to run MATLAB and the editor. This is where our main workplace is. Here you can create a new script, you can save it. You can run it as a final script where you can save it. Also here we can run a section. This added part or a section is also important. For example, here I use the command, you can use the uncomment and I can run it as a command here. You can wrap the commands, you can indent. The indentation is in the loops and advanced levels, not at this level. You can insert the section, you can insert the function or even a file. When it comes to the publishing, the publishing returns to when you are finishing your final script, if it is 1000 or 2000 lines, not in our level, as simple as that, you can just create some board or italic or more spaced, insert a line markup or you can just publish it to your you can generate a formatted output such as file from editor document. This is not our case. I'm not interested in that. And this is a little bit more advanced. The U.S. is just simple. You can break your editor, for example. I will go to custom and break my editor into four sections. This can be used in case you are working on different. Sections at the same time. You want to see your valuables and then the same time you want to work on a workplace order, on a function so you can use it as it is. This is very simple, but this is when it comes to managing the workplace from outside. However, what is the inside? The editor. Here I write my script. Let's say two plus three and stop. This is my script and hit the command window. When I run this section, I get I will get five. However, let's say I finished two plus three, two minus one, and then I run the section. I will see that the five was not deleted. It's always present on my command window. What should I do? What should I? How can I clear to my command window by its simple function? Returns to C LC, which means clear. Or you can just press it here and clear command window from this button. This is very simple. However, I have another command that give more details, which include the size, the space allocation, the class of variables. Let's say two minus one and I run. Excuse me. And I run this section. Then I press W.H.O. and it. I got that a a. Answer b c t x y. So he defined that I have no variables. Your variables are a answer b, c, t, x and y. I have no variables, so I'm not benefiting from anything. However, if I press as x equal to then uh, t equal x minus one, then I run this section. I will get t equal one if I press w h all. And until I get that my variables are the same where I have no answer. This is everything when it comes to managing the workplace. Let's move on to another section. 6. ENTERING MULTIPLE STATEMENTS: In studying multiple statements, what does it mean getting multiple statements? We can see that if I set a equal to seven, I run this section, I get eight equals seven. However, if I put the semicolon and breastfeed exclusively, the section, I get nothing because MATLAB understand that the semicolon stops. I'm not wanting anything. I'm just I deemed to some data. This is the case of the semicolon. However, this does not apply to the normal column that we have. In case I want to say. And then I can just add or keep a colon between them and drawn dissection in a very simple way. This section, I will got to be equal to two and c equals three because he understood that I defined a, B, and C. However, I won't done on my dominant. I did not add any semicolon. If I press this semicolon here and I run this section, It's clear the window before the section, I get just the because he understood Okay. Anc are defined. However, I won't be on the top. That's perfect. But if it was not a shown of the command window, does it mean that they are not present in mind MATLAB and memory? Let's see, let the window in the first case. Let's return to the US semicolon and saying a times b minus c. And let's, let's run this section. I will get 118 times b equal to 14 minus three equals 0 and solve one. Just entering the variable does not mean if it wasn't shown on the commandment go that it is not in the memory of my MATLAB. Matlab understand that, okay, 87, however, my user doesn't want it to be shown on the terminal because he simply, for us the semicolon. So this is a benefit when it comes to entering multiple statements. Thank you for listening. Let's move on to a very interesting topic. 7. MATHEMATICAL FUNCTIONS: No arriving to the mathematical functions. But before getting deep into this section, I want to go to PowerPoint and show you the mean elementary functions that MATLAB have as a pre-defined functions. In case I want to define the cosine, I have to use that COS acts the sign S-I-G-N acts dangerous TA and acts the arc cosine, arc sine the arc tangent are the same just by adding an a before the main function. What about the exponential? If I want to use an exponential, I have to use EXP. And the x, the square root is referred to as SQRT and the natural logarithm and the common logarithm or log us and blocked on x. This is when it comes to the first section, we have a second section concerning the absolute value of a variable, the signum function. In case you have a row of different numbers. For example, a having A123. We'll give an example about that. I want to ask MATLAB, what is your maximum value inside this section, he tells me the minimum. The seal on the floor are rounding functions. For example, if I have 2.3 and I want to use it as a seed, I will have to either three and the floor will give it to me as to we will see it now also using examples. You can use the round to round it to the nearest integer. The remainder after division is referred to as REM AKS. You can use phase angle and complex conjugate. These are advanced mathematical functions or elementary functions that you can use a directly without implementing the main function of cosine. Now what about the predefined constant values? We know that in math we have different values that already they are defined, for example, the main and the main obvious and well-known constant value is the pipe, which refers to 3.141591, etc. So it is referred in MATLAB as PI. However, what about the imaginary unit or the radical of minus one or square root of minus one, you just refer to it as I and j. He understand that, okay? This is an imaginary unit. J equal is an imaginary unit. What about the infinity? The infinity is referred to I and f, and this is sometimes used when you are rounding. For example, you ask MATLAB to round this, round this value to the infinity or the plus infinity, you just use the INR and NaN, not a number in case I'm defining in an advanced section, my number 76, etc. I just tell him that this is not a number, NaN this is my phone number, not a value that you can use. You have to use it as a basic statement such as name, for example, Alex are drawn. Let's go about, Let's go deep into the main mathematical functions. Let's define three variables. Let's say a equal to five and x equal to two. Y equals to eight. Anybody is simply way. Let's start conducting. Let's say Y, this Y is equal to exponent or exponential of minus a times the sine of x, sine x sine of two plus ten times square root of y. That's a very complex application formula. Let's, let's run it. I get 28.2904 in a very simple way, just defining some variables and adding complex one, I got a value in a very simple way. Let's clear the command window and use another one. For example, if I want just simply log of 142, dissection, I get 4.9558. This is simply, I don't have to define so a equal to 142 then log of a. I can use it in a very simple and fast way without any interventions or any added lines. Let's use the lockdown. I got to 0.1523. This is the common lot. Let's see some other stuff. Let's, for example, dry. It's clear the command window, Let's try the sine of pi. We said that pi is a predefined constant value, so I have to refer to it as byte here. Understand that pi equals 3.1459, etc. So sine pi divided by four. Let's see the value. I get 0.7071. This is totally correct. Let's run it as cosine. I get the same value. Let's say as tangent of Pi minus four, I should have one. What about the arc tangent? Let's say a cosine around the section 0.6675 arc sine. I got it Also 0.903040. I got 0.6658. However, if you can see that, for example, if I press cotton, cotton and drawn dissection, I get that. This is an undefined function codon for input arguments of type W. This is another in my file that it is well-known as untitled. And the third line that refers to cota and pi equals four. I know this is wrong because the cotton is well-known in month one over time. What should I do? I should stand of pi over 41 divided by turn of pi over four. Run the section I got the one. This is the proton because the ton of one over four, pi over four equals one. This is not the case here. If I change the boy, let's say pi equal to, excuse me. Let's run this section. I get one plus 63, et cetera. In case this is the first to infinity. If I wanted to divide it to get the code, I should almost get a 0 because tan Pi over two is really large. So I got a very small number which refers to getting the 0 value for the cotangent of Pi over two. So I know that MATLAB has a lot of functions. However, some functions can be replaced with others, such as the cota that it is barely used. Let's remove or clear the command window and run other stuff. Let's start by the exponential of ten. For example, under Section I got exponent of ten e to the power of 2.2 to the times ten to the power of four. Let's change the variables that I have or let's modify it a little bit dumb. Let's say I have a equals to minus 5.5, and then a b equals to 2.3, c equals to 4.9. And then ending that, let's move to the other section of the table. What about the absolute? Let's clear another type. What about the absolute of a? I just press abs of a and he gets me to running this section and give me 5.5. What is the sign of a section? He tells me it is negative one. So sine of a equals a times minus one. Let's talk about the scene of b of b. And then run this section, I get three because the scene shows me or round the number that I inserted to the plus infinity. Let's press it on a and C. Answered it is minus five. Minus five. It is between minus five on the plus infinity and minus six on the minus infinity. And that's why he showed me minus five. Let's use the floor section would shrouds the variable or the number to the minus infinity floor of B, let's say undrawn this section I will have to float of B is two because it is between 23. The flow shows me two and the sealed shows me three. Let's try some stuff. Let's move on to the round function. And the round function, there is an automatic rounding of the variables. Let's say round off to 0.3 and see what I get. I will get to because let's clear window to make it clear. Don't run this section I will get to because 0.33 is lower than five, so it takes me to the minus infinity, and so rounding to 0.3 is two. What about the rounding? See, drawn this section, I will get five because 4.99 is greater than five. The same answer. What about a? A is five, I have five then the zeros. Let's see what is the defiled rounding of five. When it comes to MATLAB, I will get minus six and always take it to the, to the lower functions because 5.55 is a middle number that I cannot act according to it. So I go to the next number here. 5.5 is referred to 00 is lower than five. I got rounding a is minus six, about 5.55556. He goes to the first 15. This is middle. I can't decide. Second five is all submitted. I cannot decide. He goes to the third 16, okay, greater than five. So I'm going to the plus infinity and now we'll get it to the minus six. Clear. Now, run the section I get minus six, that's perfect. Now and round a, let's clear it. My maximum because they are very important and they are well used when giving some advanced operations. So you can get the minimum and the maximum value and work accordingly. And in case you were sorting, for example, if you have a Ford or five values, 12367 and you are asking MATLAB to sort it. He goes by an inner function to the maximum value. He enters maximum value, he got the seven Dan, he remove it and then enter six, then enters four, understood, etc. So let's say eight equal number of matrix a 2345. That's perfect. The done, I say minimum of a run, I will get the minimum value is one. Now what about the maximum of a? I got five. So in case I changed them like six here, here minus 551. I run this section, I get the maximum as six and the minimum is minus 51. That, That's everything for the mathematical functions. Let's move on to the basic plotting. This is also a very interesting topic. 8. BASIC PLOTTING: No arriving to basic plotting, MATLAB has an excellent set of graphic tools. Plotting a given data. Or the results of computation is possibility with very few commands, without complex features and complex programming commands, you are highly encouraged to plot the mathematical functions and results of analysis as often as possible. Because sometimes when you get the results as in values, you cannot detect the trends. You cannot detect some respective points through your equation. For example, if you are computing this y equals sine x function, you can see that it is elaborating between 02 Pi the results, the plotting of your results through graphs makes it easier for you to analyze your final results. Trying to understand mathematical equations, as I previously said with the graphics, is an enjoyable and very efficient way of learning mathematics. Being able to plot mathematical functions and data freely is the most important step and this section is written to assist you to do just that. Lets remove this one and start by basic plotting how you create simple plots. By creating simple plots, you just define some coordinates having different acts and different twice. So let's say x equal 12345, then ending ed y equal minus one to four, let's say five. By this I defined five coordinates, 13, having x equal one and y equals three minus 1324455. Let's make it as minus one to make it just like monster. Okay, That's perfect. We ask MATLAB to plot it by just asking plot x and y and running the section. It takes a little bit of time and get me to figure with the first coordinate. Have been x equal one and y equals three, then x equal two, and y equals minus one, then x equals three, and y equal to the fourth one is the same and also the fifth. However, this is very simple. What about when we want to ask Pi, ask MATLAB to plot something that it is referred between two areas. For example, the sine or the cosine x functions are just limited between two endpoints, the 0 and the two pipe. How we do that? We just need to specify vectors. What interests me and why it should work on the integer between 02 Pi. So we create vector Ax. So I started by creating vector x. Vector Ax is x equal what, 02 pi, two times pi. So it is in the range between 02 Pi. However, I should add the instrumentation. I should add something that takes step on between 02 Pi. So I say 0 between two pi, then I have to increment with pi divided by 100. So we can see this function. It yields a vector that starts at 0, takes steps or increments of Pi divided by 100 and stops when to buy is reached. So x equals 0 pi over 100 to pop. Now I just ask y equal sine of x and then plot x and y. That's perfect two. Now let's drag this section and see what we will have. From 0 to one, then goes back to minus one and it returns, this is between 02 Pi. This is the sine x. In a very simple way. I can change it to cosine for example. And let's draw this section. I get the different code with the inverse of the sine. Good, That's perfect than now, however, if I want to export this photo, I chose just a graph or plot, not seeing any labels. How should I include labels inside MATLAB? Stuff is easy. The problem is also easy. I should just ask x label is between parenthesis. I should include a single quotation between it. I should ask or tell him the xlabel. So I will say it AX equal 02 times. That's perfect. What about the y label? It is in the same manner. Y label is between sine of x. That's perfect. Let's run the section. I will get sine of x and x between 0.2. And this is the labels. However, this is a graph. However, it doesn't have a title. In a very simple way. I add title, title, parenthesis, the same manner, the same pattern. Pattern is present. And between the single quotation marks, I say plot the sine function. Let's run this section now and see. Plot the sine function as a title. I get the sine of x, x between 0.2 and Pi, and then it can be returned. However, if you can see that this graph is blue, how should I do to, in order to change it? In a very simple way, I got to plot x and y and add a valuable, which is by a comma, and insert the color, let's say, Gee, and run this section again it as green. G refers to green. What about ADH, which refers to red? We have diffident stop for it in case I remove it. I just got the blue one, the random definitely one. That's perfect to know. What about multiple data sets in one plot? What should I do if I have different y's on the same max? Let's say x is between 02 pi on an increment level of pi over 100. That's perfect. Didn't know, Let's name y as y, y1 and see it as two times cosine x. It can be. Let's define y2 for example. And Y2 is the simple cosine x semicolon to end it. Now, why three equals 0.5 times cosine x? Let's see what should I have generated? However, plotting x and y would return with an error because it will just show the simple acts that we had, the first white. This is not the case that we are plotting. So I go to say X and whom? Y1. Okay, That's perfect. Then I say X and Y to X and Y free. Then I will end it. Let's remove the labels. Now. Let's just remove the labels now. Drawn this section. I will have graphs, one referring to two times x x cosine x. The second is cosine x and the 3.5th one cosine x. This is the plot. However, what about some specifications and the blood? What about specifying line styles and colors? It is possible to specify line styles, colors, and markets. For example, circles plus signs, et cetera, using the plot command plus plot IX, y-prime, than the style color market. We have different colors, black, red, blue, green, cyan, and yellow than solid dashed, dotted, dashed dots. And that no line. Also we have symbol market, the plus sign, so it'd good asterisk, point cross square diamond asset. So let's go back to the plot between X and Y, Y1. What should I include after them? I should include after the comma, the style that I want between two single quotation marks, I wanted as a double dash. Between x and y, y2, I will add double or single quotation mark, and let's say one dash. Then after X and Y three, Let's make it as dotted single marks, single quotation marks, excuse me, excuse me, and double points. Let's run this section. I have now different types. X, y, y1 is double dash, x y2 is a single dash and y three is pointed. That's perfect. No, let's just add some labels. So the y-label parenthesis done single quotations and between them cosine functions. That's perfect. What about the legend? Let's add the legend is two times sine x. This is the first one. Then comma. The second one is cosine x with a single quotation. Then the third one is 0.5 times cosine x. That's perfect. Till now. Let's add also a title. So title refers to typical example of multiple plots. That's perfect to know. Let's add some axis. Axis equals between 02 pi minus 33. So access is 0 to times by minus three. The three added and run this section. I will have first typical example of multiple plots, not appealing because of this cosine functions. I did not add any x-axis because I have the legend, the legend one, it shows me two times cosine x, cosine x and 0.5 times cosine x. That's everything when it comes to basic plotting. Let's move on to what it is main important and specification of MATLAB, the matrices. 9. MATRIX GENERATION: Welcome everyone to matrix generation. This section is really important. As I previously said, MATLAB means Matrix Laboratory. Matlab is one of the unique tools that acts with matrices in a very simple and professional and complex way where it can compute different types of matrices in a very simple and few commands. Before entering deep into the matrix, this section will be large. I'm going to define the vector. How should I include a vector into MATLAB? If vector, a row vector starts by brackets, done 12345, let's say, and ending with brackets, what is between done as an either or either space, space, either semicolon when it comes to space and column adjust at all. Now if I want to run this section, I will go just in case I put it as space. I will have the same because space refers also, excuse me, the column refers to a row. Now instead of row pressing semi-colons, what we will have is a vector v, that it is a column. So V 12345. This is when it comes to the vector. However, there is a very simple and easy way to transpose the row into a vector. The transpose function or the transpose operator is denoted denote, denoted by a single code. So what should be done as you convert a column into arrow or arrow into a column just by pressing V and a single quotation, you get it and run it. You will have it as a rope. Now, in case if it was a column, if it was at all. And I transposed it, Let's clear my command window and run it as section. I will get it as a column. So this is very simple. Now let's go back to Dr. indexing, vector, indexing. The first to checking the index of each parameter. In case you work with other programming computers or softwares, you will see that always the index starts with 0, so one refers to index 0. However, in MATLAB, life is more simple. It's simpler. Index1 refers to the first number. No need to start it with 0 and the other stops. So let's clear the command and start by indexing. So let's ask MATLAB what is on the first index of the run this section, you will tell me what, what about the third one? He would tell me three. Even if I changed here as seven, for example, I'm drawing this section, I will get seven. So the third number, the number that I inserted. So what about asking him what is in-between off the first index and the third index I started by one. Differentiate the two points. I'm saying to him from one from one to 40, I have 127. Let's wrap this section. I will have 127. What about from city two to 53 to five? Let's try this section. I will have 745. However, there is another way, if you didn't know the number of indexes that it is present in the MATLAB. You just have to press it as from 32 and there's no need to just ask or just start calculating or measuring time. So 745, Let's return this to three because we ended the index matrix. Now I will start with entering a matrix, a matrix or a vector or very similar matrix. Let's say a equals. It should start with a bracket. And then we separate what is inside a row with columns or spaces similar to the vector. And when you stop and you want to separate between the columns, if you just have to insert the semicolon sections. So let's say 123, semicolon 456, semicolon 789. Then we ended or we finish it with the matrix with the brackets exclude. This is 123456789. It refers that on the first row I have three columns in which the first one is one, the second one is two, and the third one is a three word in the second row I have 456, etc. Let's run this section. I will get a as I have it. Now. What about the matrix indexing? Changing what is inside a matrix. Let's start just by matrix indexing. In case I pressed the semicolon and I want to ask MATLAB to tell me what is inside a and the second row. Then on the first column, he would directly tell me for brand, I would get bored because this is a, I have on the second row, the first column. This is for, let's say for example, let's run this section. I will get eight, Let's 33, I will get nine. Even if I own 150, I will have three. That's perfect. Let's clear it. This is when it comes to indexing. What about when I want to change what is inside my matrix, what is inside the matrix that I injected or I inputted? One-off, let's say three of three, this is dynein one. I want to change it into 0. What should I put? I press a three of three. So inside the third row, the third column, this number, I want to change it into 0. Let's run this section. I will have 123456780. This is, this can be done in a different way where you can change the number. For example, if I wanted as a 0, let's run this section. I will have it as a 0. I want to make it as one. I can do endless stuff using it. Now. Just keep it in mind that MATLAB understands the matrix as the first letter, the variable that I inserted my matrix and that it is in my case the a, then the eye, then the number of j here, it changes this sector into the value that I told him to do so. Now what about colon operator? Colon operator is another section into matrix generation, but it is not a matrix, it is a vector. However, this technique can be used in matrix. You can see or you will see how. Let's start by coordinate operator, colon operator. I'm asking MATLAB that I am defining UX. I want the values between 05. However, I don't want it to be just randomly. I wanted add an addition or a step size of 0.5. So he will tell me that, okay, I will generate for you the numbers between 05 at a rate of 0.5. Let's try this section. I will have 11 numbers from 0 till five. I will have each difference, the 0.5. However, we have defined variables are defined commands such as the linear spacing. This is very similar to the garden operator, but it gives control over the number of points. For example, if I said y equal to learn space from 0 till five, however, at a rate of 0.5. So he tells million space x1 is, x2 is five. What is the what is the tenth time step size is 0.5. Let's clear it before and press the Run Section. I will have one times 0 empty WO vector. Excuse me. What's that? Okay, That's perfect. Line space. Let's say it is like that and run it again. One times 0 and a double row factor, there is a problem that he is taking it in another section. Clear, let's say linspace between 05 without inventing the number of human no, directly that I should insert 100 number as a deaf child, he will tell me between 05 there is 100 number. I'm telling you them at a rate of 0.05 or five. That's when it comes to linear spacing. Linear spacing is used when, for example, you are creating a router in a game or in an operation that you want the equidistance between 0 and then you just use the linspace and you indicate the number of intersections or steps, the step sizes that you want to enter these values in programming. Matlab also, now, we talked about the colon operator, the linear spacing. Now, what are those used for? I will tell you what are those in matrix, because this section is matrix generation. What happens is called an operator in a matrix is used to extract certain row or column. For example, if I want to extract something from inside my matrix, Let's return a equal. You will understand everything in a bit. 123, semicolon 456, so we call them 789, and then the matrix and the semicolon. Okay, going back to Matrix generation and colon operator, colon operator in the matrix, I said before that it is used to extract. A certain row of column. So the formula that it follows is a between rows is between k and excuse me, columns. So this is it, I want to extract from a as it is a from row to row. And I specify these numbers column till column. And let's say from column one, column two, and from, from row one to row two. From this six numbers, I want the first column, the second column. Let's try the extraction. I say I have 12451245, the first two rows. From these first two rows, I just want the first two columns. Now what about if I want a full row? For example, I want the second row all by itself. So I just directly put R2D2. I wanted from, I want all the column. Instead of putting 123456, I just removed the 13. It just needed to be simple. So a2 comma. So in the second row, I want from which column to which column or columns because I kept them as void. Run section I would have four or 56. That's clear. It in order to make sure Run Section 456. The same is about the columns in case I want all the rows. And then I went from column two, column three, he would take all the rows than just the first, the second, third column. I run this section, I will have to 35689. It is the same if I inserted 123 Iran, the assumption section, nothing differed. So clearing it now. Now moving to the same matrix however, now I want to delete a row or column. To do so, we use the same as matrix indexing that I use in order to change a value. However, I have to insert the anti operator, which refers as the opening and break, adding the brackets. So I say that I want a from the third row, from the first column, the third column. So all the columns equal void. Now I run this section, I will have just 123456. Now it is, the dated is no mode inside the a. In case I pressed of third row and second column. I will have, let's say run this section. I will have an error because index position one exceeds ADA bonds because must not exceed two. That's correct. The third row is normal present I deleted it. It is no more than the machinery of MATLAB. Matlab does not understand that. Okay, Now we want me back to a, this is not correct. It drones according to a flow of sections. So I remove this. Let's clear the command window. Now we deleted this row. What about restoring this drug store the straw using the same technique as creating the matrix. If you remember, first one I said you have to start the matrix by first specifying the vertebral not equal. Now, opening the brackets, That's perfect. A equal, something. I open the brackets. What is my first true? My first row is instantly the first row. All columns. This 1, first row, all the columns. This is my first drop. How we separate between arrow and another row by a semicolon, the same as for the second row. The second row, comma and thirst. Okay, That's perfect. This is the second door. I didn't change anything in it. Now, this is my third row that I separated with a semicolon. I say, I opened the matrix 78, Let's say nine or 0. No, let's say night. Okay, that's perfect. If I want 78 unknown, now I close the brackets and run this section and we'll have 123456789. Now in case I asked for 33, for example, in a very easy way, I will close this section before we run this session, I will have nine. Now it is back. I re-inserted in the third row that I deleted. Before we finish the one comes to the matrix deleting the story. What about transposing a matrix? Transposing a matrix is very similar to the one that we used when we transpose the column. If you remember the V 12345, that V prime. Using the single code, it turns it into a column and vice versa. This is similar to a matrix. So I'm gonna clear, let's say, let's delete all that and a prime just running this section, I will have that each row became a column. So 123 became one column, and 456, which is the second draw, became the second column, 789, this third rule became the third column. And in case now I use a semicolon and ask for a 50. For example. One, the first draw, then the third column. I will have three because a transpose does not change the value of a. I didn't say that a equal a transpose. This is not my case. I just asked MATLAB to transpose a prime. However, I didn't change my main body, but that we used before. However, if I said a equal to a prime, now I'm Dy run this session, I will have it seven because I defined a as a brand. Now there is like that and 13 is seven. That's very important to know what odd the sessions or what is the workflow that MATLAB use or understand one creating your script? Let's move on to the matrix generators. Matrix generators. We have different matrix generators. Matlab provides functions, degenerates elementary matrices, the matrix of zeros, the matrix of ones and the identity matrix are determined by functions zeros, ones and what I respectively, for example, the eye. And it returns an m by n matrix with one on the main diagonal, where i and returns an n by n squared identity matrix. The zeros, it returns an m by n matrix of zeros, the ones that are similar to the zeros and m by n matrix of one's, the diagonal. It extracts the diagonal of matrix a and the red. I'm an iterator is an m by n matrix of random numbers. I will show you that. For example, this is a, this is a, let's print it, Let's say display it on the main command window. I have 123456789. What about if I want to ask for the diagonal? The diagonal is 159, semicolon here, semicolon here, and ask diagonal of a split on determinant, I would have 159. Now, what about at ended? Let's say we have it as referred rand a because I did not define random, the random a pulsar. Now let's clear this function and ask, for example, to create a function g that it returns once. Returns one of 30 rows. How many columns? One column, so it is 111. Let's run it. I would have 111. This is the ones. So now what about C equal i, i of three? If three, it returns, I previously said it returns an m by n squared identity matrix, n by n, three by three when it is identity matrix, so the diagonal is equal to one. Let's try this section, 100010001. Now what about the zeros? So let's say d equal to zeros of two. So two rows and three columns. So I'd have six zeros. Let's run this section, but before, let's put a semicolon here. I will have six zeros, two rows of zeros, and the three columns of zeros. This one, it comes to matrix generators. This is very essential and it is a well-used and usually used when it comes to numerical simulation, numerical methods when you are trying to multiply a matrix with another MATLAB makes your life easier because if you are trying to solve it using gestured hand, you have to follow different steps and different indentation. And do you have to check the adder and according to the other, you have to change your technique. This is not the case using mockup. This software makes the life of a mathematician or a scientist's way much easier, and it is unique in MATLAB. Let's move on to the special matrices as we was, as we were talking about mathematics and algorithms, matlab provides a number of a special matrices. These matrices have interesting properties that make them useful for constructing examples and forecasting algorithms. We have different MATLAB documentation. You can check them. The most used ones by, let's say, mathematicians on the Hilbert and the inverse Hilbert matrix and the pascal matrix. These three are well used. This is everything when it comes to matrix generation. Let's move on to another session on directly hope that you understand, understood what matrix are, how we generate them, how we act with them, how we interfered, add, delete, we transpose it, how we check the index. This is really important and really essential. And even the matrix generators are also a very important, especially the diagonal, the eye and the ones. Thank you for listening. Let's move on to another section. 10. ARRAY PROPERTIES: Arriving to the ADA properties in matrix, you should understand that even matrix have arithmetic operations. Let's say for example, if I have a and B, I want to add them. I can add a plus B or B plus a. It should be valid if the a and B are of the same size. For example, if a was three by three and b is three by three, it should be the same. However, if I want to multiply a by B, it should be taken into consideration that if A's that should be A's number of columns should be equal that B's number of rows. However, even this is the same what I want a to the power of two. However, power of two, multiplication in matrices have a specific command, so I won't interfere it now. Next in this video, let's start by the simple arithmetic to plus and minus. Let's define a equals to 123 semicolon 4567 in column 6789, ending the bracket semicolon be equal to done. 102030, semicolon, 405060, semicolon 7080, and then 90. Then I close the brackets and ending it. If I say a plus b and display it on their own section, I will have 1110 plus ten, plus 23, plus 34 plus 40. This is the same. If I said Example b minus a, I will have it as 91827 different areas. I can do so because as you can see, a and B are of the same size. In case I say, let's clear this window and show you that it makes an error. If I change 90, for example, and drag this section, I will have another dimensions of arrays being contaminated or not consistent. There is another and the B, it should be 98. That's perfect when it comes to the arithmetic operations. Now what about the times, division and multiplication? This stuff are similar to the vectors are used by a times, let's say C equals a times b. However, there is a problem or there is something that indicates for MATLAB, no pay attention MATLAB, this, these are matrices is not simple variables. Actually just press the point section point or the dot stars B, I will have under display tan 409160, etcetera multiplied each index of a by the similar or corresponding index of this is the same. If I want, for example, p divided by a, this won't work unless I should insert the dot. Cheap all its time because it's dividing by their relative. Now what about if C equals a to the power of two? Should I include? Should I included? Yes, for sure, you should include the dot even if there were no matrices. And the same section, this is when it comes to the addie arithmetic operations of matrices. Now, we have different matrix functions. Let's start by, let's go to the PowerPoint and see diesem, see them. Okay, I have this determinant. It is defined by DET. So the determinant of a lead score, determinant, excuse me. Determinant of mathematicians will know that this state unless numbered in order to get the determinant. Now, the determinant of B, this is minus 1.5. Let's see clearly now and go see another function. The diagonal March. She's a diagonals of a matrix. So let's say diagonal of I previously implemented that in a different way. Not date, okay. Diagonal DIA on this section, I would have 159. What about B? I will get a section 101519. Pay attention. If B, you press it and the lowercase, you will understand that there is another diagonal of the, it's made it another function. So please don't, I just keep it as it is. Now we go to the eigenvalues or eigenvectors. This is not our case. Let's talk about the inverse matrix because avert matrix will be used in the next session when we are talking about solving linear equations. So simply inverse of a. Run this section, I will have it. This is really hard. When you see it on Matlab. You just make your life easy. All this very simple. Our other in life, this takes up to 2030 minutes in conducting on hands. And there is a huge probability of equation of adders and the huge probability of confirmation, for example, 0.3153, you just take 0.31, you won't take it as exact. So MATLAB make life in this matrix as easy as possible. I pressed particularly a command here. This everything went comes to the array properties. Let's apply what we learned an array properties and in matrix generation into solving real problems and to solving linear equations. 11. Solving Linear Equations: Now solving linear equations, I know a lot of students and a lot of people that use, that don't use MATLAB or don't know how to use MATLAB, just conduct solving linear equations using the calculator. However, in case that the variable is, number of variables increases above three or 44 or five, excuse me. Calculator is no more a helpful tool and you just have to conduct it on your hand just by trial and error using numerical simulations and linear equations. In MATLAB, you just have a very nice tool using matrices and using other operations in order to solve such equations. What should be done is let's assume that I have x, x plus two, y plus z equals to one. And plus three is four, x plus five plus six, that equals to 17 plus eight equals storm. So these are a comment, let's say to let MATLAB and tell him No, this is just a command. Don't take it into consideration. So what I have to do is I have to create two matrices, a and B. Let's say a equals to what? The first row is, one index of acts done than three. Semicolon, 456, semicolon 78, and then 0. Because index of Z in the third row is 0. This is when it comes to a. Now we create the b equals to one semicolon, semicolon one, which refers to the values of the three equations. What we have to do now is to say, or we assume that AX equals to B. This is recumbent AX equilibrium. What is the value of x? X equals to the borrower? The poet of minus one times B. This is inside parenthesis. We have two ways in order to solve. The first one is we say a equal etcetera be equal to etcetera. X equals the inverse of a times B. Let's try it on the display. We got minus 111, so x equal to minus one, y equals one, and z equal to 0. This is the same if I said x equal to a divided by b. Let's try section. Let's clear it in order to let you see it. Let's try it. Now. I have minus 11 minus 0, which is 0. So by this, we can solve linear equations. Let's say if I changed those feet, four minus one, Let's see what will be the value to be one minus 0.6667. In case I want to add it plus four z. Let's say plus k. Here, a plus k, plus k, I have to change. So now it is City. Here it is two, and now we have 41. The values are 30 minus 34, minus one. However, now we have four variables and three equations. I have to add another equation. Let's say two, x plus four, y minus set minus two K. I got it as equals to eight. I change 12334567841 semicolon to four, minus one and minus two. We changed here also to eight. Let's run it. I will have minus 5.94.61.21 minus 1.3. By this, you can add as much as you want variables and you will find a solution. Let's assume here minus plus two, plus two here, minus for odd, I have to add the value, let's say also a command, x plus two, y minus one, minus one, k plus two odd equals to minus five. I should change it now. So the first row should include also minus1. The second row should include also to the third row should include also to the fourth row should include minus four. Also I have to add a new row, city two minus one, minus one. And then to afford I have to change also the B and also in minus five. Let's run it. I will have an urge because matrix dimensions must agree. Let's close this one. I have, the minus five is here, then I close the brackets. Let's run this section. I will have four minus 4.13.5, minus 2.35, and minus 3.85. I can add as much as I want, I valuables using equations and I can solve linear equations and just a period of seconds. 12. Project Proposal: Welcome back everyone. I wish you enjoyed all the materials of introduction to matlab course. I wish it was beneficial. And you acquired the required knowledge in terms of MATLAB and matrices. At the end of each class, I suggest doing a small assessment for yourself where you can see what are your weak points. You can go back to the video. Reward should see what is the problem. You can contact me directly in case you face any problem or you had a big question or critical question concerning MATLAB and the project. I can help you to overcome it. When it comes to the project, it will be question is small question relying of two matrices where you have to perform different commands that we learned all over the course. It will start very easy. The basics, it will go a more complex in the following slides, however, it will stay as an easy too. Assume hardness project. It is not hard at all. It's not challenging at all. When it comes to the project, I am suggesting u and v of five numbers. You have to perform the following commands on MATLAB. First you have to add u and v, then multiply u by v, then reads, raise each element of u to the power of two, then divide each element of view by the corresponding element of V, also the same from V towards you. However, pay attention that when it comes to the matrices, this case the operational and mathematical operations. I'm not similar to the just numbers. Using MATLAB as the calculator. You have to remember what we are, what symbol we add an ordered for MATLAB to understand. Pay attention. I'm working with matrices not normal numbers in case student remembers that. That's perfect in case not go back to the videos. Remind yourself about it. It's really simple. And in case you didn't remind that you will do all these five questions wrong. It is essential. The sixth question you have to sort you in this slide or this bunch of questions, we will go to the formatting of the matrix. So I'm sorting you certain view as a sort. It is in the ascending form, however, sorted now in the descending fall, now create a row vector w consisting of the elements of u and v. The majority of students just freeze at this level. There's nothing hard at it. Just act with the u and v as numbers. Just add to create a matrix that is called W, where you are defining it as a two numbers. These two numbers are u and v. Now create a column vector W, in which the first row is, you add the second row is V. Find the minimum value in new and find the maximum value of u. You have to create a vector u that consists the elements of you. And you have to add a sixth element equals to 120. Now we automate imaging with you from the index seven to the index nine that are not present because you have five numbers. And the 120 that we added, a sixth number, now, seven till nine, you have to add 8410. Now, delete all the indexes between 35. I helped you in this question. I added the equal vote. However, some students just forgot that deleting is just creating an equal operation would avoid space. Now find you of three to check what will happen to the index three, it is really important. Now find the sum of you, find the product of you. I wish you are able to enjoy the course one more time and you will be able to solve this project. In the next video, I will add a solution for this project for you in case you did a mistake to correct yourself, in case you are stuck on any question to be easy for you. Thank you so much and I wish you the best of luck. 13. Project Solution: I really wish you enjoyed the project. Now let's move on to solving this project. Let's go here to project if you equal 12345 and V equals 6789, Let's go. U equals to 12345 semicolon, v equals to 678910. Semicolon. Perform the following commands on MATLAB. Add u and v as you can, no, you can't this easy. U plus v under display I got the answer 79111315. Let's clear the command. Now. Multiply each element of U by the corresponding element in V. Also at this simple, You point times V. Run the section I got at 614. Twenty four, thirty six fifty. Raise each element of u to the power of 2 or dot power of two. Let's run this section. I get 1491625. This is totally correct. Let's divide each element of U by the corresponding element of v, u divided by V. And let's clear the command in order to make the solution easier around section I have it. Now the inverse V dot divided by u. Let's run this section. I get 63.52.67 AD setting. Now I'm clearing the command to now everything's easy. Let's move on to the second section. Let's sort you how we sort you, Press, Sort you the section 12345. Now sort2 in the descending form, we sort u comma. We say these centered around this section, we got 54321. Create a row vector w consisting of the elements of u and v. How do we do that? So we just say w equals u, then we all the rows of you than space, which means we are in the same row. Let's run this section. I have from one delta1, the column vector W, in which the first row is u and the second row is V, create a column vector u, in which the first short is u and the second row is v. So I have to separate them with a semicolon. Let's clear it and run the section 123456789. That's simple. Find the minimum value in new. We go to MATLAB and brass, minimum of u. Let's run this section. I would have the answer as one. Minimum of V is six. Maximum of v should be done. The maximum of you should be five. That's totally correct. Now create a bacteria consists of the elements of U and the sixth element equals 120. What we should do in order to create this vector u equals to what do you, this we are on the same row. I want to add 120. So MATLAB understand that u is not equal to 123456 elements 120. Let's run this section. We got it. Creates you of seven to nine. So that's correct. I'm asking that selection from seventh to the ninth. Let's run this section. I will have it as drunk because I don't have index seven till night. He's asking me to create a U from seven to nine equals to 84 to1. Let's copy it from here. Go to MATLAB Control V, you from seven to nine equal to eight for ten. What does it mean? You know, is equal to 12345120 is the sixth, the seventh is eight, the eighth is four, and the ninth is that. This has now created. If you want to display you, Let's run this section. I will have it 12345128410, create you of three to five equals to void. So I'm deleting it. Now. You off from three to five. I'm deleting it as a void display. Let's run the section now I have one to the third and the fourth and the fifth are deleted than 120. And we can continue then find U of three. Now and say find or just you of three. The third index is 120th. Let's run the selection. I have 120, find the sum of u, which is very easy. Some of you and run the section I got 145. What about the product of u? Just product of you. I wish that you enjoyed this course in case you need any help, just contact me through the context that I displayed in the introduction video. Thank you so much for attending you in other courses.