PoojaMoolya: Created page with "{| border=1 ||'''Time''' ||'''Narration''' |- ||00:01 || Welcome to this tutorial on '''Vectors and Matrices''' in '''Geogebra'''. |- || 00:06 || In this tutorial, w..."

2020-10-21T07:10:28Z

Created page with "{| border=1 ||'''Time''' ||'''Narration''' |- ||00:01 || Welcome to this tutorial on '''Vectors and Matrices''' in '''Geogebra'''. |- || 00:06 || In this tutorial, w..."

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{| border=1
||'''Time'''
||'''Narration'''

|-
||00:01
|| Welcome to this tutorial on '''Vectors and Matrices''' in '''Geogebra'''.

|-
|| 00:06
|| In this tutorial, we will learn about,

How to draw a '''vector'''

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||00:11
|| Arithmetic operations on '''vectors'''

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||00:14
|| How to create a '''matrix'''

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||00:16
|| Arithmetic operations on '''matrices'''

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||00:19
|| '''Transpose''' of a '''matrix'''

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||00:22
|| '''Determinant''' of a '''matrix'''

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||00:25
|| '''Inverse''' of a '''matrix'''

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||00:28
|| Here I am using, Ubuntu Linux OS version 14.04

GeoGebra version 5.0.388.0 hyphen d.

|-
|| 00:40
|| To follow this tutorial, you should be familiar with '''Geogebra''' interface.

|-
||00:47
|| If not, for relevant '''Geogebra''' tutorials please visit our website.

|-
|| 00:52
|| Let us define a '''vector'''.

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||00:55
|| '''Vector''' is a quantity that has both '''magnitude''' and '''direction'''.

|-
|| 01:00
|| I have opened a '''GeoGebra''' window.

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|| 01:03
|| Before I start this demonstration I will change the font size to 20.

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||01:08
|| Go to '''Options '''menu, scroll down to '''Font Size'''.

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||01:12
|| From the sub-menu select '''20 point''' radio button.

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|| 01:16
|| Let us draw a '''vector'''.

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||01:19
|| Click on '''Line tool''' drop down and select '''Vector''' tool.

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||01:25
|| Click on the Origin(0,0) and drag the mouse to draw a vector '''u'''.

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|| 01:30
|| Let us draw another '''vector v''' from the origin.
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|| 01:34
|| Let us show the relation between '''vectors''' and a '''parallelogram'''.

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|| 01:39
|| Consider two '''vectors''' as two adjacent sides of a '''parallelogram. '''

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||01:43
|| Then the resultant of these '''vectors''' is the diagonal of the '''parallelogram'''.

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|| 01:48
|| Let's add the vectors '''u''' and '''v'''.

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||01:51
|| In the input bar, type '''u+v''' and press '''Enter'''.

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||01:57
|| Here '''vector w''', represents addition of the '''vectors u''' and '''v'''.

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|| 02:02
|| Let's show that '''vector w''' is '''diagonal''' of the '''parallelogram'''.

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|| 02:07
|| To demonstrate this, let's complete the '''parallelogram'''.

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|| 02:11
|| Click on the '''Line''' drop-down and select '''Vector from Point''' tool.

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|| 02:17
|| Click on point '''B''' and '''vector v'''.

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|| 02:21
|| The new '''vector a''' same as '''vector v ''' is drawn.

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|| 02:25
|| Click on point '''C''' and '''vector u''' .

|-
|| 02:29
|| The new '''vector b''' same as vector '''u,''' is drawn.
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|| 02:33
|| Using '''Move''' tool, move the labels.

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|| 02:37
|| '''Parallelogram A B Bdash C ''' is completed.

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|| 02:42
|| Notice that '''diagonal A Bdash ''' represents sum of '''vectors u''' and '''v'''.

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|| 02:48
|| Press '''CTRL+Z''' to undo the process.

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|| 02:53
|| Retain the '''vector u'''.

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|| 02:55
|| Now we have '''vector u''' on '''Graphics view'''.

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|| 02:59
|| '''Cartesian coordinates''' of the '''vector''' are shown in the '''Algebra view'''.

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||03:04
|| Here values of '''magnitude''' and angle of '''vector u''' are displayed.

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|| 03:10
|| If we move point '''B''', values change accordingly.

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|| 03:15
|| In the '''Algebra view,''' right click on '''vector u'''.

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|| 03:19
|| A sub-menu appears.

Select '''Polar coordinates'''.

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|| 03:24
|| Observe the '''coordinates''' in the '''polar''' form.

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|| 03:27
|| To change the values manually, right click on point '''B'''.

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|| 03:31
|| Select '''Polar coordinates'''.

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|| 03:34
|| Double-click on point '''B''' to change the values.

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|| 03:38
|| Type '''5''' as '''magnitude'''; '''50''' as angle and press '''Enter'''.

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|| 03:45
|| Notice the change in '''magnitude''' and angle of '''vector u'''.

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|| 03:49
|| Let us multiply a '''vector''' by a '''scalar'''.

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|| 03:53
|| Type '''2u''' in the '''input bar''' and press '''Enter.'''

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|| 03:57
|| The '''magnitude''' of new '''vector''' is equal to 2u.

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|| 04:01
|| Type ''' minus 2u''' and press '''Enter'''.

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|| 04:05
|| The '''magnitude''' of new '''vector''' is '''2u''', but in opposite direction.

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|| 04:10
|| To view the new '''vectors''', use '''Zoom Out''' tool from tool bar.

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|| 04:17
|| As an assignment,

Subtract the '''vectors u''' and '''v'''

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|| 04:22
|| Divide a '''vector''' by a '''scalar'''.

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|| 04:25
|| Now we will move on to '''matrices'''.

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|| 04:28
|| A '''matrix''' is an ordered set of numbers.

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|| 04:31
|| It is listed in a rectangular form as ‘m’ rows and ‘n’ columns.

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|| 04:36
|| A unit matrix is I equal to 1

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|| 04:40
|| It has m equal to n equal to 1 and '''element''' is also 1.

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|| 04:47
|| An '''identity matrix''' is a '''square matrix'''.

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|| 04:51
|| It has all the diagonal elements as 1 and rest of the elements as 0.

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|| 04:56
|| X is a 2 by 2 '''identity matrix''' and

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|| 05:00
|| Y is a 3 by 3 '''identity matrix'''.

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|| 05:04
|| In GeoGebra, we can create a '''matrix''' using:

'''Spreadsheet view ''' , '''CAS view ''' and '''Input bar'''.

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||05:13
|| Let's open a new window.

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|| 05:18
|| To create '''matrices''', we will close '''Graphics''' view and open '''Spreadsheet''' view.

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|| 05:26
|| Type the '''elements''' of the '''matrix''' in the '''spreadsheet'''.

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|| 05:30
|| Type the elements in the cells starting from '''A1'''.

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|| 05:34
|| Type the first row '''elements''' as 1 3 2.

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|| 05:42
|| Similarly type the remaining '''elements'''.

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|| 05:47
|| To create a '''matrix''', select the '''matrix elements.'''

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|| 05:51
|| Click on''' List''' drop-down and select '''Matrix'''.

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|| 05:56
|| '''Matrix''' dialog-box opens.

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|| 05:59
|| In the '''Name''' text box, type the name of '''matrix''' as '''A'''.

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|| 06:04
|| Click on '''Create''' button.

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|| 06:07
|| A 3 by 3 '''matrix''' is displayed in the '''Algebra view.'''

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|| 06:11
|| Let us create the same '''matrix''' using '''CAS view'''.

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|| 06:15
|| To open '''CAS view''', go to '''View''' menu, click on '''CAS''' check box.

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|| 06:23
|| In the first box, type the '''elements''' of the '''matrix''' as shown and press '''Enter'''.

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|| 06:30
|| Here, inner curly brackets represent different rows.

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|| 06:35
|| Close the '''CAS view'''.

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|| 06:37
|| Similarly, we will create another 3 by 3 '''matrix B'''.

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|| 06:42
|| Type the '''elements''' of the '''matrix''' in the '''spreadsheet''' as shown.

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|| 06:46
|| To create a '''matrix''', select the '''elements''' and right click.

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|| 06:51
|| A sub-menu opens.

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|| 06:53
|| Navigate to '''Create''' and select '''Matrix'''.

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||06:58
|| To rename the '''matrix''', right click on the '''matrix''' in the '''Algebra View'''.

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|| 07:03
|| Select '''Rename'''.

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|| 07:05
|| '''Rename''' dialog-box appears.

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|| 07:08
|| Type the name as '''B''' and click '''OK'''.

|-
|| 07:14
|| We can add or subtract '''matrices''' only if they are of the same order.

|-
||07:19
|| Now we will add the '''matrices A''' and '''B'''.

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|| 07:22
|| In the '''input bar''', type '''A + B'''and press '''Enter'''.

|-
|| 07:28
|| Addition '''matrix M1''' is displayed in the '''Algebra view'''.

|-
|| 07:32
|| Now we will see multiplication of '''matrices'''.

|-
|| 07:36
|| Two '''matrices X''' and '''Y '''can be multiplied if,

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|| 07:40
|| number of columns of '''X''' is equal to the number of rows of '''Y'''.

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|| 07:45
|| '''X''' is '''m by n matrix, Y''' is '''n by p matrix'''.

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|| 07:50
|| '''X into Y '''is a '''matrix ''' of order '''m by p'''.

|-
|| 07:54
|| Let us will create a 3 by 2 '''matrix C''' using the '''input bar.'''

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|| 07:59
|| In the '''input bar''', type the '''matrix C''' as shown and press '''Enter'''.

|-
|| 08:06
|| Let us multiply the '''matrices A''' and '''C'''.

|-
|| 08:10
|| In the '''input bar''', type, '''A asterisk C ''' and press '''Enter'''.

|-
|| 08:16
|| Product of '''matrices A''' and '''C''' is displayed as '''M2''' in the '''Algebra view'''.

|-
|| 08:22
|| As an assignment,

Subtract '''matrices''' , Multiply '''matrices''' of same order and different order.

|-
|| 08:30
|| To show '''transpose''' of '''matrix A'''- in the '''input bar''', type: '''transpose'''.

Select '''Transpose Matrix'''
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|| 08:38
|| Type '''A''' in place of '''Matrix''' and press '''Enter'''.

|-
|| 08:42
|| Transpose of a '''matrix M3''' is displayed in the '''Algebra view'''.

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|| 08:47
|| Now, we will show '''determinant''' of '''matrix A'''.

|-
|| 08:51
|| In the input bar, type '''determinant'''

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|| 08:54
|| Select '''Determinant Matrix'''

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|| 08:57
|| Type '''A''' in place of '''Matrix ''' and press '''Enter'''.

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|| 09:01
|| Value of '''Determinant''' of '''matrix A''' is displayed in the '''Algebra view'''.

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|| 09:06
|| A '''square matrix P ''' has an '''inverse,''' only if the '''determinant''' of '''P''' is not equal to zero '''

|-
|| 09:13
|| Now, we show '''inverse''' of '''matrix '''.

|-
|| 09:16
|| In the '''input bar''', type, '''invert'''

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|| 09:19
|| Select '''Invert Matrix'''

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||09:22
|| Type '''A''' in place of '''Matrix''' and press '''Enter'''.

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|| 09:26
|| Drag the border of '''Algebra view''' to see the inverse matrix

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|| 09:31
|| Inverse of '''matrix A''', '''M4''' is displayed in the '''Algebra view.'''

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|| 09:36
|| If '''determinant''' value of a '''matrix''' is zero, its '''inverse''' does not exist.

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|| 09:41
|| For this we will create a new '''matrix D'''.

|-
||09:45
|| Type the '''elements''' of the '''matrix''' as shown.

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|| 09:49
|| Select the '''elements''' and right click to open a sub-menu.

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|| 09:53
|| Select '''Create '''and then select '''Matrix'''.

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|| 09:58
|| Rename the '''matrix M5''' in the '''Algebra view''' as '''D'''.

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|| 10:03
|| Using the '''input bar''', let us find the '''determinant'''.

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|| 10:07
|| Type '''determinant'''

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|| 10:09
|| Select '''Determinant Matrix'''

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|| 10:12
|| Type '''D''' in place of '''Matrix''' and press '''Enter'''.

|-
|| 10:16
|| We see that '''determinant''' of '''matrix D''' is zero.

|-
|| 10:20
|| Now, in the '''input bar''', type, '''Invert(D)'''

and press '''Enter'''.

|-
|| 10:26
|| '''L1 undefined''' is displayed in the '''Algebra view'''.

|-
|| 10:30
|| This indicates that inverse of '''matrix D''' cannot be determined.
|-
|| 10:36
|| As an assignment,

Find the '''determinant''' and '''inverse''' of '''Matrices B ''' and '''C'''.

|-
|| 10:43
|| Let's summarize.

|-
|| 10:45
|| In this tutorial, we have learnt,

How to draw a '''vector'''

|-
|| 10:49
|| Arithmetic operations on '''vectors'''

|-
|| 10:52
|| How to create a '''matrix'''

|-
|| 10:54
|| Arithmetic operations on '''matrices'''

|-
|| 10:58
|| '''Transpose''' of a '''matrix'''

|-
|| 11:01
|| '''Determinant''' of a '''matrix'''

|-
|| 11:04
|| '''Inverse''' of a '''matrix''' .

|-
||11:06
|| The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

|-
|| 11:14
|| The '''Spoken Tutorial Project ''' team:

conducts workshops using spoken tutorials and gives certificates on passing online tests.

|-
|| 11:22
|| For more details, please write to us.

|-
|| 11:25
|| Do you have questions in THIS Spoken Tutorial?

Please visit this site

|-
|| 11:30
|| Choose the minute and second where you have the question

|-
|| 11:34
|| Explain your question briefly

|-
|| 11:37
|| Someone from our team will answer them.

|-
|| 11:40
|| The Spoken Tutorial forum is for specific questions on this tutorial

|-
|| 11:45
|| Please do not post unrelated and general questions on them

This will help reduce the clutter

|-
|| 11:52
|| With less clutter, we can use these discussion as instructional material.

|-
|| 11:57
|| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

|-
|| 12:03
|| More information on this mission is available at this link.

|-
|| 12:08
|| This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.
|-
|}

Applications-of-GeoGebra/C2/Vectors-and-Matrices/English-timed - Revision history

PoojaMoolya: Created page with "{| border=1 ||'''Time''' ||'''Narration''' |- ||00:01 || Welcome to this tutorial on '''Vectors and Matrices''' in '''Geogebra'''. |- || 00:06 || In this tutorial, w..."