Scilab/C2/Matrix-Operations/Gujarati - Revision history

Gaurav at 10:01, 21 July 2014

2014-07-21T10:01:26Z

Pratik kamble at 09:39, 26 June 2014

2014-06-26T09:39:17Z

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Jyotisolanki at 08:53, 27 December 2013

2013-12-27T08:53:55Z

Krupali at 06:49, 19 November 2013

2013-11-19T06:49:44Z

Krupali at 06:22, 19 November 2013

2013-11-19T06:22:33Z

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Krupali: Created page with ' {| Border=1 || Time || Narration |- | 00.03 | | Welcome to the spoken tutorial on Matrix Operations. |- |00.07 | | At the end of this spoken tutorial, you will be able t…'

2013-11-19T04:36:21Z

Created page with ' {| Border=1 || Time || Narration |- | 00.03 | | Welcome to the spoken tutorial on Matrix Operations. |- |00.07 | | At the end of this spoken tutorial, you will be able t…'

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{| Border=1

|| Time

|| Narration

|-

| 00.03

| | Welcome to the spoken tutorial on Matrix Operations.

|-

|00.07

| | At the end of this spoken tutorial, you will be able to:

|-

| 00.10

| | Access the elements of Matrix

|-

| 00.13

| |Determine the determinant, inverse and eigen values of a matrix.

|-

| 00.19

| |Define special matrices.

|-

| 00.23

| | Perform elementary row operations.

|-

| 00.25

| | Solve the system of “linear equations”.

|-

|00.29

| | The preequisites are

|-

| 00.31

| |Scilab should be installed on your system.

|-

| 00.34

| |''You should have listened to the Spoken Tutorial: Getting started with Scilab and '''Vector Operations.

|-

| 00.42

| |I am using Windows 7 operating system and Scilab 5.2.2 for demonstration.

|-

| 00.50

| | Start Scilab by double-clicking on the Scilab icon present on yourDesktop.

|-

| 00.59

| |It is suggested '''that '''the user should''' practice this tutorial in Scilab simultaneously while pausing the video at regular intervals of time.'''

|-

| 01.09

| | Recall that in the Spoken Tutorial, 'Vector Operations',

|-

| 01.12

| | matrix E was defined as E = [5 19 15;8 22 36]and press enter

|-

| 01.37

| |Let us now see how to address individual elements of a matrix, separately.

|-

| 01.42

| |To access the element in the first row and second column, type: E(1,2) and press enter

|-

| 01.56

| | It is easy to extract an entire row or an entire column of a matrix in Scilab .

|-

| 02.03

| |For example, first row of E can be obtained using the following command: E1 = E(1,:) and press enter

|-

| 02.24

| |The command returns all the elements of the first row in the order of their appearance in the row.

|-

| 02.30

| |Colon, when used alone, refers to all the elements of row or column, depending upon whether it appears as a first or a second entry respectively inside the bracket.

|-

| 02.44

| | Also, any subset of a matrix can be extracted using a colon (“:”).

|-

| 02.49

| |For example, the set of elements starting from second to third columns of E can be obtained using the following command:

|-

| 03.01

| |-->E2 = E(:,2:3) close the bracket and press enter

|-

| 03.18

| |In the above, the second entry in the bracket, that is, "2 colon 3" makes a reference to elements from column 2 to column 3.

|-

|03.28

| | If the size of the matrix is not known $ symbol can be used to extarct the last row or column of that matrix.

|-

| 03.38

| |For example to extract all rows of the last column of the matrix E, we will type

|-

| 03.46

| |--->E last column = E(:,$) close the bracket and press enter

|-

| 04.06

| |Now, let us learn how to calculate the determinant of a square matrix using the command “det”

|-

| 04.13

| |Recall that in the Spoken Tutorial, Vector Operations, we had defined A as

|-

| 04.20

| |A=[1 2 - 1; - 2 - 6 4; - 1 - 3 3] close the square bracket and press enter

|-

| 04.50

| |Let us calculate the determinant of A by the command det(A) and press Enter.

|-

| 05.00

|| To calculate the inverse and the eigenvalues of a matrix, the commands, “inv” and “spec” respectively, can be used.

|-

| 05.09

|| For example: inv(A) gives the inverse of A and spec(A) gives the eigen values of A

|-

| 05.29

| |See 'help spec' to see how eigenvectors can also be obtained using this command.

|-

| 05.35

| |Square or cube of a square matrix A can be calculated by simply typing A^2 or A^3 '''respectively'''.

|-

| 05.52

| |A caret symbol is used to raise a matrix to power, like in ordinary arithmetic operations. In our keyboard, it is obtained by pressing shift+6.

|-

| 06.05

| | '''Please pause the tutorial now and attempt exercise number one given with the video.'''

|-

| 06.18

| | Certain special matrices can also be created in Scilab:

|-

| 06.24

| |For example a matrix of zeros with 3 rows and 4 columns can be created using “zeros” command

|-

| 06.36

| |zeros(3,4) and press enter

|-

| 06.48

| |A matrix of all ones can be created with “ones” command as follows

|-

| 06.53

| |ones(2,4) gives a matrix of all ones

|-

| 07.02

| |It is easy to create an identity matrix using “eye” command:

|-

| 07.07

| |eye(4,4) gives a 4 by 4 identity matrix

|-

| 07.17

| |A user may need a matrix consisting of pseudo random numbers. It can be generated using the “rand” command as follows:

|-

| 07.25

| |p=rand(2,3) and press enter

|-

| 07.39

| | In linear systems, one of the important sets of operations a user carries out on matrices are the elementary row and column operations.

|-

| 07.55

| |These operations involve executing row operations on a matrix to make entries below a nonzero number, zero. This can be done easily in Scilab.

|-

| 08.08

| |Recall that in the Spoken Tutorial,Vector Operations, we had defined the matrix P as follows.

|-

| 08.18

| |P = [1 2 3;4 11 6]close the square bracket and press enter

|-

| 08.34

| |Let us consider an example where the element in the second row, first column is to be transformed to zero using elementary row and column operation.

|-

| 08.45

| |The operation can be executed by multiplying the first row by 4 and subtracting it from the second row as in the following command:

|-

| 08.57

| |P(2,:) = P(2,:) - 4*P(1,:) and press enter

|-

| 09.29

| The procedure can be extended to larger systems and to other forms of elementary column operations.

|-

| 09.35

| |Rows and columns can be easily appended to matrices.

|-

| 09.39

| |For example, to append a row containing [5 5 -2] to P, the following command is used:

|-

|09.49

| |T = [P; [5 5 -2]] close both the square bracket and press enter

|-

| 10.15

| |The semicolon after P states that the anything after it should go to the next row. '

|-

| 10.20

| |This is expected in the way a matrix is defined.

|-

| 10.24

| |As an exercise, please pause here and check if the brackets around the new row, in the command just executed, are really required.

|-

| 10.34

| |Matrix notations are used while solving equations.

|-

| 10.41

|| Let us solve the following set of linear equations:

|-

| 10.44

| |x1 + 2 x2 − x3 = 1

|-

| 10.48

| |− 2 x1 − 6 x2 + 4 x3 = − 2

|-

| 10.54

| |− x1 − 3 x2 + 3 x3 = 1

|-

| 11.00

| |The above set of equations can be written in the Ax = b form.

|-

| 11.05

| | The solution is then given as inverse of A times b

|-

| 11.11

| |Let us solve the set of equations.

|-

| 11.15

| |A is defined as A = [1 2 -1;-2 -6 4;-1 -3 3] close the square bracket and press enter

|-

| 11.46

| |B can be defined as b = [1;-2;1]close the square bracket and press enter

|-

| 12.04

| |The solution, x, can be obtained using x = inv(A)*b

|-

| 12.20

| |It is worth noting that it is a small letter 'i' in the command, 'inv'.

|-

| 12.27

| |Alternatively, the same result can be achieved using a backslash operation in Scilab.

|-

| 12.33

| |Lets do this in Scilab x = A\b and press enter.

|-

| 12.45

| |It gives the same result. Type "help backslash" and "help inv" in Scilab to know more about individual advantages and disadvantages.

|-

| 12.55

| |The integrity of the solution can be verified by back substitution, that is, by calculating Ax-b:

|-

|13.05

|A*x-b

|-

| 13.10

| |The above exercise verifies the result achieved earlier.

|-

| 13.14

| |It is possible that in some systems the above verification exercise may not yield a matrix with *exact* zeros as its elements due to intermediate floating point operations.

|-

| 13.27

| |However, one will indeed get a very small number, typically of the order of 10 raised to -16

|-

| 13.35

| '''Please pause the tutorial now and attempt exercise number two given with the video.'''

|-

| 13.49

| '''This brings us to the end of this spoken tutorial on Matrix Operation.'''

|-

| 13.54

| |'''There are many other functions in Scilab which will be covered in other spoken tutorials.

|-

| 13.59

| Keep watching the Scilab links.'''

|-

| 14.02

| |'''In this tutorial we have learnt'''

|-

| 14.04

| | '''To access the element of the matrix using the colon operator'''

|-

| 14.08

| | '''Calculate the inverse of a matrix using the 'inv' command or by backslash'''

|-

| 14.14

| |'''Calculate the derterminant of matrix using 'det' command.'''

|-

| 14.19

| | '''Calculate eigen values of a matrix using 'spec' command.'''

|-

| 14.24

| | '''Define a matrix having all the elements one, Null Matrix,

|-

| 14.29

| Identity matrix and a matrix with random elements by using functions ones(), zeros(), eye(), rand() respectively'''

|-

| 14.39

| | '''Solve the system of linear equations.'''

|-

| 14.43

| | '''This spoken tutorial has been created by the Free and Open Source Software in Science and Engineering Education(FOSSEE). '''

|-

| 14.51

| | '''More information on the FOSSEE project could be obtained from [http://fossee.in/ http://fossee.in] or [http://scilab.in/ ] '''

|-

| 14.59

| | '''Supported by the National Mission on Eduction through ICT, MHRD, Government of India. '''

|-

| 15.05

| | '''For more information, visit: [http://spoken-tutorial.org/NMEICT-Intro http://spoken-tutorial.org/NMEICT-Intro] '''

|-

| 15.15

| |'''This is Anuradha Amrutkar from IIT Bombay signing off.'''

|-

|

| |'''Thank you for joining. Goodbye.'''

|}

@@ Line 1: / Line 1: @@
 {| Border=1
-|| Time
+|| '''Time'''
-|| Narration
+|| '''Narration'''
 |-

@@ Line 186: / Line 186: @@
 | 04.20
-| |A=[1 2 - 1; - 2 - 6 4; - 1 - 3 3] ચોરસ કૌસ બંધ કરો અને એન્ટર ડબાઓ.
+| |A=[1 2 -1; - 2 -6 4; -1 -3 3] ચોરસ કૌસ બંધ કરો અને એન્ટર ડબાઓ.
 |-
@@ Line 369: / Line 369: @@
 | 10.48
-| |− 2 x1 − 6 x2 + 4 x3 = − 2
+| |−2 x1 − 6 x2 + 4 x3 = − 2
 |-
@@ Line 375: / Line 375: @@
 | 10.54
-| |− x1 − 3 x2 + 3 x3 = 1
+| |−x1 −3 x2 + 3 x3 = 1
 |-

@@ Line 454: / Line 454: @@
 | 13.14
-| |It is possible that in some systems the above verification exercise may not yield a matrix with *exact* zeros as its elements due to intermediate floating point operations.
+| |એ શક્ય છે કે કેટલીક સિસ્ટમોમાં ઉપરનો ચકાસણી અભ્યાસ મધ્યસ્થી ફ્લોટિંગ પોઇન્ટના કારણે *ચોક્કસ* zeros સાથે મેટ્રિક્સ જનરેટ ન કરી શકે.
-−
 |-
 | 13.27
-| |However, one will indeed get a very small number, typically of the order of 10 raised to -16
+| |જો કે, તે ખરેખર ખૂબ જ નાની સંખ્યા મેળવી શકે છે, સામાન્ય રીતે, 10 રેઇઝ ટુ -16 ના ઓર્ડરમાં.
-−
 |-
 | 13.35
-| '''Please pause the tutorial now and attempt exercise number two given with the video.'''
+| '''હવે આ ટ્યુટોરીયલ અટકાવો અને વિડિઓ સાથે આપવામાં આવેલ અભ્યાસ નમ્બર ૨ કરો.'''
 |-
@@ Line 472: / Line 470: @@
 | 13.49
-| '''This brings us to the end of this spoken tutorial on Matrix Operation.'''
+| '''Matrix Operation પરનું આ સ્પોકન ટ્યુટોરીયલ અહીં સમાપ્ત થાય છે..'''
 |-
@@ Line 478: / Line 476: @@
 | 13.54
-| |'''There are many other functions in Scilab which will be covered in other spoken tutorials.
+| |સાઈલેબના ઘણા અન્ય ફન્કશન છે જે આપણે બીજા અન્ય સ્પોકન ટ્યુટોરિયલ્સ માં જોઈશું.
-−
 |-
 | 13.59
-| Keep watching the Scilab links.'''
+| સાઈલેબ લીનક્સ જોતા રહો.
-−
 |-
 | 14.02
-| |'''In this tutorial we have learnt'''
+| |આ ટ્યુટોરીયલમાં આપણે શીખ્યા,
 |-
@@ Line 496: / Line 492: @@
 | 14.04
-| | '''To access the element of the matrix using the colon operator'''
+| |કોલોન ઓપરેટરની મદદથી મેટ્રીક્સના એલિમેન્ટો એક્સેસ કરવા.
 |-
@@ Line 502: / Line 498: @@
 | 14.08
-| | '''Calculate the inverse of a matrix using the 'inv' command or by backslash'''
+| | 'inv' આદેશ અથવા બેકસ્લેશની મદદથી મેત્રીક્ષનું ઇન્વર્શ શોધવું.
 |-
@@ Line 508: / Line 504: @@
 | 14.14
-| |'''Calculate the derterminant of matrix using 'det' command.'''
+| |'ડેટ' આદેશની મદદથી મેટ્રિક્સના નિર્ણાયકની ગણતરી કરવી.
 |-
@@ Line 514: / Line 510: @@
 | 14.19
-| | '''Calculate eigen values of a matrix using 'spec' command.'''
+| |'spec' આદેશની મદદથી મેટ્રિક્સની eigen વેલ્યુઝની ગણતરી કરવી.
 |-
@@ Line 520: / Line 516: @@
 | 14.24
-| | '''Define a matrix having all the elements one, Null Matrix,
+| |બધા એલિમેન્ટો 1 હોય, નલ મેટ્રીક્સ,
 |-
@@ Line 526: / Line 522: @@
 | 14.29
-| Identity matrix and a matrix with random elements by using functions ones(), zeros(), eye(), rand() respectively'''
+| Identity મેટ્રીક્સ અને રેન્ડમ વેલ્યુઝ સાથે મેટ્રીક્સ, આ તમામ અનુક્રમે ones(), zeros(), eye(), rand() ફન્કશનનો ઉપયોગ કરી મેટ્રીક્સ વ્યાખ્યાયિત કરો.
 |-
@@ Line 532: / Line 528: @@
 | 14.39
-| | '''Solve the system of linear equations.'''
+| | '''રેખીય સમીકરણોની સિસ્ટમ ઉકેલો.'''
 |-
@@ Line 538: / Line 534: @@
 | 14.43
-| | '''This spoken tutorial has been created by the Free and Open Source Software in Science and Engineering Education(FOSSEE). '''
+| |આ સ્પોકન ટ્યુટોરીયલ  Free and Open Source Software in Science and Engineering Education (FOSSEE) દ્વારા બનાવવામાં આવ્યું છે.
-−
 |-
 | 14.51
-| | '''More information on the FOSSEE project could be obtained from [http://fossee.in/ http://fossee.in] or [http://scilab.in/ ] '''
+| |''' FOSSEE પ્રોજેક્ટ પર વધુ માહિતી [http://fossee.in/ http://fossee.in] અથવા [http://scilab.in/]'' માંથી મેળવી શકાય છે'
-−
 |-
 | 14.59
-| | '''Supported by the National Mission on Eduction through ICT, MHRD, Government of India. '''
+| | '''જે આઇસીટી, એમએચઆરડી, ભારત સરકાર દ્વારા શિક્ષણ પર નેશનલ મિશન ધ્વારા આધારભૂત છે'''
 |-
@@ Line 556: / Line 550: @@
 | 15.05
-| | '''For more information, visit: [http://spoken-tutorial.org/NMEICT-Intro http://spoken-tutorial.org/NMEICT-Intro] '''
+| | '''વધુ માહિતી માટે, [http://spoken-tutorial.org/NMEICT-Intro http://spoken-tutorial.org/NMEICT-Intro] જુઓ'''
 |-
@@ Line 562: / Line 556: @@
 | 15.15
-| |'''This is Anuradha Amrutkar from IIT Bombay signing off.'''
+| |આઈઆઈટી બોમ્બે તરફથી ભાષાંતર કરનાર હું કૃપાલી પરમાર વિદાય લઉં છું.
 |-
@@ Line 568: / Line 562: @@
+|
-| |'''Thank you for joining. Goodbye.'''
+| |જોડવા બદલ આભાર.
 |}