Scilab/C4/Linear-equations-Gaussian-Methods/English-timed - Revision history

Sandhya.np14 at 09:44, 20 November 2017

2017-11-20T09:44:08Z

PoojaMoolya at 05:54, 10 March 2017

2017-03-10T05:54:35Z

Sandhya.np14 at 14:14, 27 February 2015

2015-02-27T14:14:14Z

Sandhya.np14 at 11:58, 27 February 2015

2015-02-27T11:58:36Z

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Gaurav at 12:24, 10 July 2014

2014-07-10T12:24:41Z

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PoojaMoolya: Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 |Welcome to the spoken tutorial on ''' “Solving System of Linear Equations using Gauss Elimination a…'

2014-03-11T09:47:46Z

Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 |Welcome to the spoken tutorial on ''' “Solving System of Linear Equations using Gauss Elimination a…'

New page

{| Border=1

|| 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

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| 00.31
|with '''Scilab 5.3.3''' version

|-
| 00.36
| To practise this tutorial, a learner should have basic knowledge of '''Scilab'''

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|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

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|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.

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| 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.'''

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| 03.15
|And we state that '''A''' and '''b''' are the '''arguments''' of the function '''naive gaussian elimination.'''

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| 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.'''

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| 04.32

| This code converts the '''augmented matrix to upper triangular matrix''' form.

|-

| 04.39

|Finally, we perform '''back substitution.'''

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| 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.

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| 05.10

|On the '''console,''' we have a prompt to enter the value of the '''coefficient matrix.'''

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| 05.17

|So we enter the values of '''matrix A.'''

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|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 '''

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| 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

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| 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

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| 06.16

| '''naive gaussian elimination open paranthesis A comma b close paranthesis '''

|-

| 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'''

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| 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.

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| 07.14

| We do this to get '''diagonal element''' equal to one.

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| 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 squre 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 paranthesis A comma b close paranthesis '''

|-

| 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 summarises 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.

@@ Line 85: / Line 85: @@
 | 01:16
-||along with the '''constants b one''' to  '''b n ''' of the system of equations
+||along with the '''constants b one''' to  '''b m ''' of the system of equations
 |-

@@ Line 6: / Line 6: @@
 |-
 | 00:01
-|Dear Friends,
+|Dear Friends, Welcome to the spoken tutorial on '''Solving System of Linear Equations using Gauss Elimination and Gauss-Jordan Methods'''.
 |-
-| 00:02
+| 00:12
-|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:
@@ Line 321: / Line 317: @@
 |05:53
-||Press '''Enter'''.
+||Press '''Enter'''.  The next prompt is for '''matrix b.'''
-−
-|-
-−
-| 05:54
-−
-| The next prompt is for '''matrix b.'''
 |-
@@ Line 333: / Line 323: @@
 | 05:57
-|So we type
+|So we type  '''open square bracket four point seven two semi colon three point one semi colon two point nine one close square bracket.'''
-−
-|-
-−
-| 05:58
-−
-| '''open square bracket four point seven two semi colon three point one semi colon two point nine one close square bracket.'''
 |-
@@ Line 544: / Line 528: @@
 | 09:22
-|So we type
+|So we type '''open square bracket zero point seven comma one seven two five semi colon'''
-−
-|-
-−
-| 09:23
-−
-|'''open square bracket zero point seven comma one seven two five semi colon'''
 |-

@@ Line 161: / Line 161: @@
 |-
 | 02:43
-| It will display a message to the user and get the values of '''A''' and '''B''' matrices.
+| It will display a message to the user and get the values of '''A''' and '''b''' matrices.
 |-
@@ Line 216: / Line 216: @@
 | 03:57
-| 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.'''
 |-
@@ Line 222: / Line 222: @@
 | 04:05
-| If '''n''' and '''m''' one are not equal, we display a message
+| If '''n''' and '''m one''' are not equal, we display a message
 |-
@@ Line 303: / Line 303: @@
 |05:20
-|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 '''
 |-
@@ Line 371: / Line 371: @@
 |-
 | 06:32
-|Next we shall study the '''Gauss- Jordan method.'''
+|Next we shall study the '''Gauss-Jordan method.'''
 |-
@@ Line 377: / Line 377: @@
 | 06:36
-| In '''Gauss – Jordan Method''',
+| In '''Gauss–Jordan Method''',
 |-
@@ Line 389: / Line 389: @@
 | 06:42
-| To do this place the coefficient '''matrix A''' and the right hand side '''matrix b''' together in one '''matrix.'''
+| To do this, place the coefficient '''matrix A''' and the right hand side '''matrix b''' together in one '''matrix.'''
 |-
@@ Line 455: / Line 455: @@
 | 07:55
-|Then we get the '''A''' and '''b matrix''' using the '''input function. '''
+|Then we get the '''A''' and '''b matrix''' using the '''input''' function.
 |-
@@ Line 496: / Line 496: @@
 | 08:45
-|Then we create a '''matrix''' of zeros called '''x''' with '''m''' rows and ''' s columns.'''
+|Then we create a '''matrix''' of '''zeros''' called '''x''' with '''m''' rows and '''s columns.'''
 |-
@@ Line 508: / Line 508: @@
 | 08:54
-|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.
 |-
@@ Line 604: / Line 604: @@
 | 10:08
-|Press '''Enter'''
+|Press '''Enter'''.
 |-
@@ Line 628: / Line 628: @@
 | 10:21
-|Develop '''Scilab''' code for solving system of '''linear equations'''
+|Develop '''Scilab''' code for solving system of '''linear equations'''.
 |-
 |10:25
-| Find the value of the unknown variables of a system of '''linear equations'''
+| Find the value of the unknown variables of a system of '''linear equations'''.
 |-