Difference between revisions of "Scilab/C4/Linear-equations-Gaussian-Methods/English-timed"
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| − | |Welcome to the spoken tutorial on | + | |Welcome to the spoken tutorial on '''Solving System of Linear Equations using Gauss Elimination and Gauss-Jordan Methods'''. |
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| − | |Develop '''Scilab''' code to solve linear equations | + | |Develop '''Scilab''' code to solve linear equations. |
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|'''Ubuntu 12.04''' as the operating system | |'''Ubuntu 12.04''' as the operating system | ||
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| 00:31 | | 00:31 | ||
| − | |with '''Scilab 5.3.3''' version | + | |with '''Scilab 5.3.3''' version. |
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| 00:36 | | 00:36 | ||
| − | | To | + | | To practice this tutorial, a learner should have basic knowledge of '''Scilab''' |
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| − | | | + | | finite collection of '''linear equations''' of the same set of '''variables'''. |
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|01:00 | |01:00 | ||
| − | |Let us study '''Gauss elimination method''' | + | |Let us study '''Gauss elimination method'''. |
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|01:06 | |01:06 | ||
|'''A x equal to b''' | |'''A x equal to b''' | ||
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|01:10 | |01:10 | ||
| − | |'''n''' unknowns | + | |'''n''' unknowns. |
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| − | || in one '''matrix''' called the '''augmented matrix''' | + | || in one '''matrix''' called the '''augmented matrix'''. |
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| We do so by performing row wise manipulation of the '''matrix.''' | | We do so by performing row wise manipulation of the '''matrix.''' | ||
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|01:40 | |01:40 | ||
| − | |Let us solve this system of equations using '''Gaussian elimination method''' | + | |Let us solve this system of equations using '''Gaussian elimination method'''. |
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|This defines how many digits should be displayed in the answer. | |This defines how many digits should be displayed in the answer. | ||
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| 02:04 | | 02:04 | ||
| − | |The letter 'e' within single quotes denotes that the answer should be displayed in '''scientific notation''' | + | |The letter 'e' within single quotes denotes that the answer should be displayed in '''scientific notation'''. |
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| The argument '''zero''' specifies that '''Scilab''' need not do anything if the variables are redefined. | | The argument '''zero''' specifies that '''Scilab''' need not do anything if the variables are redefined. | ||
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|Then we define the function '''naive gaussian elimination.''' | |Then we define the function '''naive gaussian elimination.''' | ||
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| 03:15 | | 03:15 | ||
|And we state that '''A''' and '''b''' are the '''arguments''' of the function '''naive gaussian elimination.''' | |And we state that '''A''' and '''b''' are the '''arguments''' of the function '''naive gaussian elimination.''' | ||
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|Similarly we can use '''m one''' and '''p''' for matrix '''b.''' | |Similarly we can use '''m one''' and '''p''' for matrix '''b.''' | ||
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|| Then we have to determine if the matrices are compatible with each other and | || Then we have to determine if the matrices are compatible with each other and | ||
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| If '''n''' and '''n one''' are not equal, then we display a message that '''Matrix A must be square.''' | | If '''n''' and '''n one''' are not equal, then we display a message that '''Matrix A must be square.''' | ||
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| If '''n''' and '''m''' one are not equal, we display a message | | If '''n''' and '''m''' one are not equal, we display a message | ||
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| '''incompatible dimension of A and b.''' | | '''incompatible dimension of A and b.''' | ||
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| If the matrices are compatible, we place matrices '''A''' and '''b''' in one matrix, '''C.''' | | If the matrices are compatible, we place matrices '''A''' and '''b''' in one matrix, '''C.''' | ||
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||This matrix '''C''' is called '''augmented matrix. ''' | ||This matrix '''C''' is called '''augmented matrix. ''' | ||
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| This code converts the '''augmented matrix to upper triangular matrix''' form. | | This code converts the '''augmented matrix to upper triangular matrix''' form. | ||
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|Finally, we perform '''back substitution.''' | |Finally, we perform '''back substitution.''' | ||
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| Then once one variable is solved, we take this variable to solve the other variables. | | Then once one variable is solved, we take this variable to solve the other variables. | ||
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||Thus the system of '''linear equations''' is solved. | ||Thus the system of '''linear equations''' is solved. | ||
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|On the '''console,''' we have a prompt to enter the value of the '''coefficient matrix.''' | |On the '''console,''' we have a prompt to enter the value of the '''coefficient matrix.''' | ||
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|So we enter the values of '''matrix A.''' | |So we enter the values of '''matrix A.''' | ||
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|Type '''square bracket three point four one space one point two three space minus one point zero nine semi colon ''' | |Type '''square bracket three point four one space one point two three space minus one point zero nine semi colon ''' | ||
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| '''two point seven one space two point one four space one point two nine semi colon ''' | | '''two point seven one space two point one four space one point two nine semi colon ''' | ||
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| '''one point eight nine space minus one point nine one space minus one point eight nine close square bracket.''' | | '''one point eight nine space minus one point nine one space minus one point eight nine close square bracket.''' | ||
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| − | ||Press '''Enter''' | + | ||Press '''Enter'''. |
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| − | | '''open square bracket four point seven two semi colon three point one semi colon two point nine one close square bracket. ''' | + | | '''open square bracket four point seven two semi colon three point one semi colon two point nine one close square bracket.''' |
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| − | |Press '''Enter''' | + | |Press '''Enter'''. |
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| Then we call the function by typing | | Then we call the function by typing | ||
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| − | | '''naive gaussian elimination open | + | | '''naive gaussian elimination open parenthesis A comma b close parenthesis ''' |
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| − | | Press '''Enter''' | + | | Press '''Enter'''. |
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| − | | In '''Gauss – Jordan Method''' | + | | In '''Gauss – Jordan Method''', |
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| − | | | + | | the first step is to form the '''augmented matrix.''' |
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| In diagonal form, only the elements '''a i i ''' are non-zero. Rest of the elements are zero. | | In diagonal form, only the elements '''a i i ''' are non-zero. Rest of the elements are zero. | ||
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| − | |Let us solve this example using '''Gauss- Jordan Method.''' | + | |Let us solve this example using '''Gauss-Jordan Method.''' |
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| − | |We get the size of '''matrix A''' and store it in '''m''' and '''n''' | + | |We get the size of '''matrix A''' and store it in '''m''' and '''n'''. |
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| − | |Similarly, we get the size of '''matrix b''' and store it in '''r''' and '''s''' | + | |Similarly, we get the size of '''matrix b''' and store it in '''r''' and '''s'''. |
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|we divide the right hand side part of '''augmented matrix''' by the corresponding '''diagonal element to get the value of each variable.''' | |we divide the right hand side part of '''augmented matrix''' by the corresponding '''diagonal element to get the value of each variable.''' | ||
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| − | |'''open square bracket zero point seven comma one seven two five semi colon ''' | + | |'''open square bracket zero point seven comma one seven two five semi colon''' |
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| − | |Press '''Enter''' | + | |Press '''Enter'''. |
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| − | |So we type '''open | + | |So we type '''open square bracket one seven three nine semi colon''' |
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| − | |'''three point two seven one close square bracket''' | + | |'''three point two seven one close square bracket'''. |
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| − | |Press '''Enter ''' | + | |Press '''Enter'''. |
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| − | |'''Gauss Jordan Elimination open | + | |'''Gauss Jordan Elimination open parenthesis A comma b close parenthesis ''' |
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|Press '''Enter''' | |Press '''Enter''' | ||
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|In this tutorial, we have learnt to: | |In this tutorial, we have learnt to: | ||
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| − | | Watch the video available at the link shown below | + | | Watch the video available at the link shown below. |
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| − | | It | + | | It summarizes the Spoken Tutorial project. |
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| − | ||If you do not have good bandwidth, you can download and watch it | + | ||If you do not have good bandwidth, you can download and watch it. |
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| − | ||The spoken tutorial project Team | + | ||The spoken tutorial project Team: |
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| − | ||Conducts workshops using spoken tutorials | + | ||Conducts workshops using spoken tutorials. |
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| − | ||Gives certificates to those who pass an online test | + | ||Gives certificates to those who pass an online test. |
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|10:52 | |10:52 | ||
| − | ||For more details, please write to conatct@spoken-tutorial.org | + | ||For more details, please write to conatct@spoken-tutorial.org. |
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| − | |Spoken Tutorial Project is a part of the Talk to a Teacher project | + | |Spoken Tutorial Project is a part of the Talk to a Teacher project. |
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| − | |More information on this mission is available at http://spoken-tutorial.org/NMEICT-Intro | + | |More information on this mission is available at http://spoken-tutorial.org/NMEICT-Intro. |
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| − | |This is Ashwini Patil signing off. | + | |This is Ashwini Patil, signing off. |
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Revision as of 17:28, 27 February 2015
| Time | Narration |
| 00:01 | Dear Friends, |
| 00:02 | Welcome to the spoken tutorial on Solving System of Linear Equations using Gauss Elimination and Gauss-Jordan Methods. |
| 00:12. | At the end of this tutorial, you will learn how to: |
| 00:15 | Solve system of linear equations using Scilab |
| 00:20 | Develop Scilab code to solve linear equations. |
| 00:25 | To record this tutorial, I am using |
| 00:27 | Ubuntu 12.04 as the operating system |
| 00:31 | with Scilab 5.3.3 version. |
| 00:36 | To practice this tutorial, a learner should have basic knowledge of Scilab |
| 00:40 | and should know how to solve Linear Equations. |
| 00:45 | To learn Scilab, please refer to the relevant tutorials available on the Spoken Tutorial website. |
| 00:52 | A system of linear equations is a |
| 00:55 | finite collection of linear equations of the same set of variables. |
| 01:00 | Let us study Gauss elimination method. |
| 01:04 | Given a system of equations |
| 01:06 | A x equal to b |
| 01:08 | with m equations and |
| 01:10 | n unknowns. |
| 01:12 | We write the coefficients of the variables a one to a n |
| 01:16 | along with the constants b one to b n of the system of equations |
| 01:22 | in one matrix called the augmented matrix. |
| 01:27 | How do we convert the augmented matrix to an upper triangular form matrix? |
| 01:33 | We do so by performing row wise manipulation of the matrix. |
| 01:40 | Let us solve this system of equations using Gaussian elimination method. |
| 01:45 | Before we solve the system, let us go through the code for Gaussian elimination method. |
| 01:52 | The first line of the code is format e comma twenty. |
| 01:58 | This defines how many digits should be displayed in the answer. |
| 02:04 | The letter 'e' within single quotes denotes that the answer should be displayed in scientific notation. |
| 02:12 | The number twenty is the number of digits that should be displayed. |
| 02:17 | The command funcprot is used to let Scilab know what to do when variables are redefined. |
| 02:26 | The argument zero specifies that Scilab need not do anything if the variables are redefined. |
| 02:33 | Other arguments are used to issue warnings or errors if the variables are redefined. |
| 02:40 | Next we use the input function. |
| 02:43 | It will display a message to the user and get the values of A and B matrices. |
| 02:51 | The message should be placed within double quotes. |
| 02:55 | The matrices that the user enters, will be stored in the variables A and b. |
| 03:02 | Here A is the coefficient matrix and b is the right-hand-side matrix or the constants matrix. |
| 03:11 | Then we define the function naive gaussian elimination. |
| 03:15 | And we state that A and b are the arguments of the function naive gaussian elimination. |
| 03:22 | We store the output in variable x. |
| 03:27 | Then we find the size of matrices A and b using the size command. |
| 03:34 | Since they are two dimensional matrices, we use n and n one to store the size of matrix A. |
| 03:42 | Similarly we can use m one and p for matrix b. |
| 03:48 | Then we have to determine if the matrices are compatible with each other and |
| 03:53 | if A is a square matrix. |
| 03:57 | If n and n one are not equal, then we display a message that Matrix A must be square. |
| 04:05 | If n and m one are not equal, we display a message |
| 04:10 | incompatible dimension of A and b. |
| 04:15 | If the matrices are compatible, we place matrices A and b in one matrix, C. |
| 04:23 | This matrix C is called augmented matrix. |
| 04:28 | The next block of code performs forward elimination. |
| 04:32 | This code converts the augmented matrix to upper triangular matrix form. |
| 04:39 | Finally, we perform back substitution. |
| 04:42 | Once the upper triangular matrix is obtained, we take the last row and find the value of the variable in that row. |
| 04:52 | Then once one variable is solved, we take this variable to solve the other variables. |
| 04:59 | Thus the system of linear equations is solved. |
| 05:03 | Let us save and execute the file. |
| 05:06 | Switch to Scilab console to solve the example. |
| 05:10 | On the console, we have a prompt to enter the value of the coefficient matrix. |
| 05:17 | So we enter the values of matrix A. |
| 05:20 | Type square bracket three point four one space one point two three space minus one point zero nine semi colon |
| 05:33 | two point seven one space two point one four space one point two nine semi colon |
| 05:41 | one point eight nine space minus one point nine one space minus one point eight nine close square bracket. |
| 05:53 | Press Enter. |
| 05:54 | The next prompt is for matrix b. |
| 05:57 | So we type |
| 05:58 | open square bracket four point seven two semi colon three point one semi colon two point nine one close square bracket. |
| 06:10 | Press Enter. |
| 06:13 | Then we call the function by typing |
| 06:16 | naive gaussian elimination open parenthesis A comma b close parenthesis |
| 06:24 | Press Enter. |
| 06:26 | The solution to the system of linear equations is shown on Scilab console. |
| 06:32 | Next we shall study the Gauss- Jordan method. |
| 06:36 | In Gauss – Jordan Method, |
| 06:38 | the first step is to form the augmented matrix. |
| 06:42 | To do this place the coefficient matrix A and the right hand side matrix b together in one matrix. |
| 06:50 | Then we perform row operations to convert matrix A to diagonal form. |
| 06:56 | In diagonal form, only the elements a i i are non-zero. Rest of the elements are zero. |
| 07:05 | Then we divide the diagonal element and corresponding element of right hand side element, by the diagonal element. |
| 07:14 | We do this to get diagonal element equal to one. |
| 07:19 | The resulting value of the elements of each row of the right hand side matrix gives the value of each variable. |
| 07:27 | Let us solve this example using Gauss-Jordan Method. |
| 07:33 | Let us look at the code first. |
| 07:36 | The first line of the code uses format function to specify the format of the displayed answers. |
| 07:44 | The parameter e specifies the answer should be in scientific notation. |
| 07:49 | Twenty (20) denotes that only twenty digits should be displayed. |
| 07:55 | Then we get the A and b matrix using the input function. |
| 08:00 | We define the function Gauss Jordan Elimination with input arguments A and b and output argument x. |
| 08:11 | We get the size of matrix A and store it in m and n. |
| 08:17 | Similarly, we get the size of matrix b and store it in r and s. |
| 08:23 | If the sizes of A and b are not compatible, we display an error on the console using error function. |
| 08:33 | Then we perform row operations to get diagonal form of the matrix. |
| 08:38 | Here pivot refers to the first non-zero element of a column. |
| 08:45 | Then we create a matrix of zeros called x with m rows and s columns. |
| 08:52 | Once we have the diagonal form, |
| 08:54 | we divide the right hand side part of augmented matrix by the corresponding diagonal element to get the value of each variable. |
| 09:04 | We store the value of each variable in x. |
| 09:08 | Then we return the value of x. |
| 09:11 | Finally, we end the function. |
| 09:13 | Now let us save and execute the function. |
| 09:18 | The prompt requires us to enter the value of matrix A. |
| 09:22 | So we type |
| 09:23 | open square bracket zero point seven comma one seven two five semi colon |
| 09:31 | zero point four three five two comma minus five point four three three close square bracket. |
| 09:41 | Press Enter. |
| 09:43 | The next prompt is for vector b. |
| 09:45 | So we type open square bracket one seven three nine semi colon |
| 09:51 | three point two seven one close square bracket. |
| 09:55 | Press Enter. |
| 09:58 | Then we call the function by typing |
| 10:01 | Gauss Jordan Elimination open parenthesis A comma b close parenthesis |
| 10:08 | Press Enter |
| 10:10 | The values of x one and x two are shown on the console. |
| 10:15 | Let us summarize this tutorial. |
| 10:18 | In this tutorial, we have learnt to: |
| 10:21 | Develop Scilab code for solving system of linear equations |
| 10:25 | Find the value of the unknown variables of a system of linear equations |
| 10:32 | Watch the video available at the link shown below. |
| 10:35 | It summarizes the Spoken Tutorial project. |
| 10:38 | If you do not have good bandwidth, you can download and watch it. |
| 10:43 | The spoken tutorial project Team: |
| 10:45 | Conducts workshops using spoken tutorials. |
| 10:48 | Gives certificates to those who pass an online test. |
| 10:52 | For more details, please write to conatct@spoken-tutorial.org. |
| 10:59 | Spoken Tutorial Project is a part of the Talk to a Teacher project. |
| 11:03 | It is supported by the National Mission on Eduction through ICT, MHRD, Government of India. |
| 11:10 | More information on this mission is available at http://spoken-tutorial.org/NMEICT-Intro. |
| 11:21 | This is Ashwini Patil, signing off. |
| 11:23 | Thank you for joining. |
