https://script.spoken-tutorial.org/index.php?title=Applications-of-GeoGebra/C2/Vectors-and-Matrices/English-timed&feed=atom&action=historyApplications-of-GeoGebra/C2/Vectors-and-Matrices/English-timed - Revision history2024-03-29T13:34:22ZRevision history for this page on the wikiMediaWiki 1.23.17https://script.spoken-tutorial.org/index.php?title=Applications-of-GeoGebra/C2/Vectors-and-Matrices/English-timed&diff=54075&oldid=prevPoojaMoolya: 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<p>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..."</p>
<p><b>New page</b></p><div>{| border=1<br />
||'''Time''' <br />
||'''Narration''' <br />
<br />
|-<br />
||00:01<br />
|| Welcome to this tutorial on '''Vectors and Matrices''' in '''Geogebra'''. <br />
<br />
|- <br />
|| 00:06<br />
|| In this tutorial, we will learn about, <br />
<br />
How to draw a '''vector''' <br />
<br />
|- <br />
||00:11<br />
|| Arithmetic operations on '''vectors''' <br />
<br />
|- <br />
||00:14<br />
|| How to create a '''matrix''' <br />
<br />
|- <br />
||00:16<br />
|| Arithmetic operations on '''matrices'''<br />
<br />
|- <br />
||00:19<br />
|| '''Transpose''' of a '''matrix''' <br />
<br />
|- <br />
||00:22<br />
|| '''Determinant''' of a '''matrix''' <br />
<br />
|- <br />
||00:25<br />
|| '''Inverse''' of a '''matrix''' <br />
<br />
|- <br />
||00:28<br />
|| Here I am using, Ubuntu Linux OS version 14.04 <br />
<br />
GeoGebra version 5.0.388.0 hyphen d. <br />
<br />
|- <br />
|| 00:40<br />
|| To follow this tutorial, you should be familiar with '''Geogebra''' interface. <br />
<br />
|- <br />
||00:47<br />
|| If not, for relevant '''Geogebra''' tutorials please visit our website. <br />
<br />
|- <br />
|| 00:52<br />
|| Let us define a '''vector'''. <br />
<br />
|- <br />
||00:55<br />
|| '''Vector''' is a quantity that has both '''magnitude''' and '''direction'''. <br />
<br />
|- <br />
|| 01:00<br />
|| I have opened a '''GeoGebra''' window. <br />
<br />
|- <br />
|| 01:03<br />
|| Before I start this demonstration I will change the font size to 20. <br />
<br />
|- <br />
||01:08<br />
|| Go to '''Options '''menu, scroll down to '''Font Size'''. <br />
<br />
|- <br />
||01:12<br />
|| From the sub-menu select '''20 point''' radio button. <br />
<br />
|- <br />
|| 01:16<br />
|| Let us draw a '''vector'''. <br />
<br />
|- <br />
||01:19<br />
|| Click on '''Line tool''' drop down and select '''Vector''' tool. <br />
<br />
|- <br />
||01:25<br />
|| Click on the Origin(0,0) and drag the mouse to draw a vector '''u'''. <br />
<br />
|- <br />
|| 01:30<br />
|| Let us draw another '''vector v''' from the origin. <br />
|- <br />
|| 01:34<br />
|| Let us show the relation between '''vectors''' and a '''parallelogram'''. <br />
<br />
|- <br />
|| 01:39<br />
|| Consider two '''vectors''' as two adjacent sides of a '''parallelogram. ''' <br />
<br />
|- <br />
||01:43<br />
|| Then the resultant of these '''vectors''' is the diagonal of the '''parallelogram'''. <br />
<br />
|- <br />
|| 01:48<br />
|| Let's add the vectors '''u''' and '''v'''. <br />
<br />
|- <br />
||01:51<br />
|| In the input bar, type '''u+v''' and press '''Enter'''. <br />
<br />
|- <br />
||01:57<br />
|| Here '''vector w''', represents addition of the '''vectors u''' and '''v'''. <br />
<br />
|- <br />
|| 02:02<br />
|| Let's show that '''vector w''' is '''diagonal''' of the '''parallelogram'''. <br />
<br />
|- <br />
|| 02:07<br />
|| To demonstrate this, let's complete the '''parallelogram'''. <br />
<br />
|- <br />
|| 02:11<br />
|| Click on the '''Line''' drop-down and select '''Vector from Point''' tool. <br />
<br />
|- <br />
|| 02:17<br />
|| Click on point '''B''' and '''vector v'''. <br />
<br />
|- <br />
|| 02:21<br />
|| The new '''vector a''' same as '''vector v ''' is drawn. <br />
<br />
|- <br />
|| 02:25<br />
|| Click on point '''C''' and '''vector u''' .<br />
<br />
|- <br />
|| 02:29<br />
|| The new '''vector b''' same as vector '''u,''' is drawn. <br />
|- <br />
|| 02:33<br />
|| Using '''Move''' tool, move the labels. <br />
<br />
|- <br />
|| 02:37<br />
|| '''Parallelogram A B Bdash C ''' is completed. <br />
<br />
|- <br />
|| 02:42<br />
|| Notice that '''diagonal A Bdash ''' represents sum of '''vectors u''' and '''v'''. <br />
<br />
|- <br />
|| 02:48<br />
|| Press '''CTRL+Z''' to undo the process. <br />
<br />
|- <br />
|| 02:53<br />
|| Retain the '''vector u'''. <br />
<br />
|- <br />
|| 02:55<br />
|| Now we have '''vector u''' on '''Graphics view'''. <br />
<br />
|- <br />
|| 02:59<br />
|| '''Cartesian coordinates''' of the '''vector''' are shown in the '''Algebra view'''. <br />
<br />
|- <br />
||03:04<br />
|| Here values of '''magnitude''' and angle of '''vector u''' are displayed. <br />
<br />
|- <br />
|| 03:10<br />
|| If we move point '''B''', values change accordingly. <br />
<br />
|- <br />
|| 03:15<br />
|| In the '''Algebra view,''' right click on '''vector u'''. <br />
<br />
|- <br />
|| 03:19<br />
|| A sub-menu appears. <br />
<br />
Select '''Polar coordinates'''. <br />
<br />
|- <br />
|| 03:24<br />
|| Observe the '''coordinates''' in the '''polar''' form. <br />
<br />
|- <br />
|| 03:27<br />
|| To change the values manually, right click on point '''B'''. <br />
<br />
|- <br />
|| 03:31<br />
|| Select '''Polar coordinates'''. <br />
<br />
|- <br />
|| 03:34<br />
|| Double-click on point '''B''' to change the values. <br />
<br />
|- <br />
|| 03:38<br />
|| Type '''5''' as '''magnitude'''; '''50''' as angle and press '''Enter'''. <br />
<br />
|- <br />
|| 03:45<br />
|| Notice the change in '''magnitude''' and angle of '''vector u'''. <br />
<br />
|- <br />
|| 03:49<br />
|| Let us multiply a '''vector''' by a '''scalar'''. <br />
<br />
|- <br />
|| 03:53<br />
|| Type '''2u''' in the '''input bar''' and press '''Enter.''' <br />
<br />
|- <br />
|| 03:57<br />
|| The '''magnitude''' of new '''vector''' is equal to 2u. <br />
<br />
|- <br />
|| 04:01<br />
|| Type ''' minus 2u''' and press '''Enter'''. <br />
<br />
|- <br />
|| 04:05<br />
|| The '''magnitude''' of new '''vector''' is '''2u''', but in opposite direction. <br />
<br />
|- <br />
|| 04:10<br />
|| To view the new '''vectors''', use '''Zoom Out''' tool from tool bar. <br />
<br />
|- <br />
|| 04:17<br />
|| As an assignment, <br />
<br />
Subtract the '''vectors u''' and '''v''' <br />
<br />
|- <br />
|| 04:22<br />
|| Divide a '''vector''' by a '''scalar'''. <br />
<br />
|- <br />
|| 04:25<br />
|| Now we will move on to '''matrices'''. <br />
<br />
|- <br />
|| 04:28<br />
|| A '''matrix''' is an ordered set of numbers. <br />
<br />
|- <br />
|| 04:31<br />
|| It is listed in a rectangular form as ‘m’ rows and ‘n’ columns. <br />
<br />
|- <br />
|| 04:36<br />
|| A unit matrix is I equal to 1 <br />
<br />
|- <br />
|| 04:40<br />
|| It has m equal to n equal to 1 and '''element''' is also 1. <br />
<br />
|- <br />
|| 04:47<br />
|| An '''identity matrix''' is a '''square matrix'''. <br />
<br />
|- <br />
|| 04:51<br />
|| It has all the diagonal elements as 1 and rest of the elements as 0. <br />
<br />
|- <br />
|| 04:56<br />
|| X is a 2 by 2 '''identity matrix''' and <br />
<br />
|- <br />
|| 05:00<br />
|| Y is a 3 by 3 '''identity matrix'''. <br />
<br />
|- <br />
|| 05:04<br />
|| In GeoGebra, we can create a '''matrix''' using: <br />
<br />
'''Spreadsheet view ''' , '''CAS view ''' and '''Input bar'''. <br />
<br />
|- <br />
||05:13<br />
|| Let's open a new window. <br />
<br />
|- <br />
|| 05:18<br />
|| To create '''matrices''', we will close '''Graphics''' view and open '''Spreadsheet''' view. <br />
<br />
|- <br />
|| 05:26<br />
|| Type the '''elements''' of the '''matrix''' in the '''spreadsheet'''. <br />
<br />
|- <br />
|| 05:30<br />
|| Type the elements in the cells starting from '''A1'''. <br />
<br />
|- <br />
|| 05:34<br />
|| Type the first row '''elements''' as 1 3 2. <br />
<br />
|- <br />
|| 05:42<br />
|| Similarly type the remaining '''elements'''. <br />
<br />
|- <br />
|| 05:47<br />
|| To create a '''matrix''', select the '''matrix elements.''' <br />
<br />
|- <br />
|| 05:51<br />
|| Click on''' List''' drop-down and select '''Matrix'''. <br />
<br />
|- <br />
|| 05:56<br />
|| '''Matrix''' dialog-box opens. <br />
<br />
|- <br />
|| 05:59<br />
|| In the '''Name''' text box, type the name of '''matrix''' as '''A'''. <br />
<br />
|- <br />
|| 06:04<br />
|| Click on '''Create''' button. <br />
<br />
|- <br />
|| 06:07<br />
|| A 3 by 3 '''matrix''' is displayed in the '''Algebra view.''' <br />
<br />
|- <br />
|| 06:11<br />
|| Let us create the same '''matrix''' using '''CAS view'''. <br />
<br />
|- <br />
|| 06:15<br />
|| To open '''CAS view''', go to '''View''' menu, click on '''CAS''' check box. <br />
<br />
|- <br />
|| 06:23<br />
|| In the first box, type the '''elements''' of the '''matrix''' as shown and press '''Enter'''. <br />
<br />
|- <br />
|| 06:30<br />
|| Here, inner curly brackets represent different rows. <br />
<br />
|- <br />
|| 06:35<br />
|| Close the '''CAS view'''.<br />
<br />
|- <br />
|| 06:37<br />
|| Similarly, we will create another 3 by 3 '''matrix B'''. <br />
<br />
|- <br />
|| 06:42<br />
|| Type the '''elements''' of the '''matrix''' in the '''spreadsheet''' as shown. <br />
<br />
|- <br />
|| 06:46<br />
|| To create a '''matrix''', select the '''elements''' and right click. <br />
<br />
|- <br />
|| 06:51<br />
|| A sub-menu opens. <br />
<br />
|- <br />
|| 06:53<br />
|| Navigate to '''Create''' and select '''Matrix'''. <br />
<br />
|- <br />
||06:58<br />
|| To rename the '''matrix''', right click on the '''matrix''' in the '''Algebra View'''. <br />
<br />
|- <br />
|| 07:03<br />
|| Select '''Rename'''. <br />
<br />
|- <br />
|| 07:05<br />
|| '''Rename''' dialog-box appears. <br />
<br />
|- <br />
|| 07:08<br />
|| Type the name as '''B''' and click '''OK'''. <br />
<br />
|- <br />
|| 07:14<br />
|| We can add or subtract '''matrices''' only if they are of the same order. <br />
<br />
|- <br />
||07:19<br />
|| Now we will add the '''matrices A''' and '''B'''. <br />
<br />
|- <br />
|| 07:22<br />
|| In the '''input bar''', type '''A + B'''and press '''Enter'''. <br />
<br />
|- <br />
|| 07:28<br />
|| Addition '''matrix M1''' is displayed in the '''Algebra view'''. <br />
<br />
|- <br />
|| 07:32<br />
|| Now we will see multiplication of '''matrices'''. <br />
<br />
|- <br />
|| 07:36<br />
|| Two '''matrices X''' and '''Y '''can be multiplied if, <br />
<br />
|- <br />
|| 07:40<br />
|| number of columns of '''X''' is equal to the number of rows of '''Y'''. <br />
<br />
|- <br />
|| 07:45<br />
|| '''X''' is '''m by n matrix, Y''' is '''n by p matrix'''. <br />
<br />
|- <br />
|| 07:50<br />
|| '''X into Y '''is a '''matrix ''' of order '''m by p'''. <br />
<br />
|- <br />
|| 07:54<br />
|| Let us will create a 3 by 2 '''matrix C''' using the '''input bar.''' <br />
<br />
|- <br />
|| 07:59<br />
|| In the '''input bar''', type the '''matrix C''' as shown and press '''Enter'''. <br />
<br />
|- <br />
|| 08:06<br />
|| Let us multiply the '''matrices A''' and '''C'''. <br />
<br />
|- <br />
|| 08:10<br />
|| In the '''input bar''', type, '''A asterisk C ''' and press '''Enter'''. <br />
<br />
|- <br />
|| 08:16<br />
|| Product of '''matrices A''' and '''C''' is displayed as '''M2''' in the '''Algebra view'''. <br />
<br />
|- <br />
|| 08:22<br />
|| As an assignment, <br />
<br />
Subtract '''matrices''' , Multiply '''matrices''' of same order and different order. <br />
<br />
|- <br />
|| 08:30<br />
|| To show '''transpose''' of '''matrix A'''- in the '''input bar''', type: '''transpose'''. <br />
<br />
Select '''Transpose Matrix''' <br />
|- <br />
|| 08:38<br />
|| Type '''A''' in place of '''Matrix''' and press '''Enter'''. <br />
<br />
|- <br />
|| 08:42<br />
|| Transpose of a '''matrix M3''' is displayed in the '''Algebra view'''. <br />
<br />
|- <br />
|| 08:47<br />
|| Now, we will show '''determinant''' of '''matrix A'''. <br />
<br />
|- <br />
|| 08:51<br />
|| In the input bar, type '''determinant''' <br />
<br />
|- <br />
|| 08:54<br />
|| Select '''Determinant Matrix''' <br />
<br />
|- <br />
|| 08:57<br />
|| Type '''A''' in place of '''Matrix ''' and press '''Enter'''. <br />
<br />
|- <br />
|| 09:01<br />
|| Value of '''Determinant''' of '''matrix A''' is displayed in the '''Algebra view'''. <br />
<br />
|- <br />
|| 09:06<br />
|| A '''square matrix P ''' has an '''inverse,''' only if the '''determinant''' of '''P''' is not equal to zero '''<br />
<br />
|- <br />
|| 09:13<br />
|| Now, we show '''inverse''' of '''matrix '''. <br />
<br />
|- <br />
|| 09:16<br />
|| In the '''input bar''', type, '''invert''' <br />
<br />
|- <br />
|| 09:19<br />
|| Select '''Invert Matrix''' <br />
<br />
|- <br />
||09:22<br />
|| Type '''A''' in place of '''Matrix''' and press '''Enter'''. <br />
<br />
|- <br />
|| 09:26<br />
|| Drag the border of '''Algebra view''' to see the inverse matrix <br />
<br />
|- <br />
|| 09:31<br />
|| Inverse of '''matrix A''', '''M4''' is displayed in the '''Algebra view.''' <br />
<br />
|- <br />
|| 09:36<br />
|| If '''determinant''' value of a '''matrix''' is zero, its '''inverse''' does not exist. <br />
<br />
|- <br />
|| 09:41<br />
|| For this we will create a new '''matrix D'''. <br />
<br />
|- <br />
||09:45<br />
|| Type the '''elements''' of the '''matrix''' as shown. <br />
<br />
|- <br />
|| 09:49<br />
|| Select the '''elements''' and right click to open a sub-menu. <br />
<br />
|- <br />
|| 09:53<br />
|| Select '''Create '''and then select '''Matrix'''. <br />
<br />
|- <br />
|| 09:58<br />
|| Rename the '''matrix M5''' in the '''Algebra view''' as '''D'''. <br />
<br />
|- <br />
|| 10:03<br />
|| Using the '''input bar''', let us find the '''determinant'''. <br />
<br />
|- <br />
|| 10:07<br />
|| Type '''determinant''' <br />
<br />
|- <br />
|| 10:09<br />
|| Select '''Determinant Matrix''' <br />
<br />
|- <br />
|| 10:12<br />
|| Type '''D''' in place of '''Matrix''' and press '''Enter'''. <br />
<br />
|- <br />
|| 10:16<br />
|| We see that '''determinant''' of '''matrix D''' is zero. <br />
<br />
|- <br />
|| 10:20<br />
|| Now, in the '''input bar''', type, '''Invert(D)''' <br />
<br />
and press '''Enter'''. <br />
<br />
|- <br />
|| 10:26<br />
|| '''L1 undefined''' is displayed in the '''Algebra view'''. <br />
<br />
|- <br />
|| 10:30<br />
|| This indicates that inverse of '''matrix D''' cannot be determined. <br />
|- <br />
|| 10:36<br />
|| As an assignment, <br />
<br />
Find the '''determinant''' and '''inverse''' of '''Matrices B ''' and '''C'''. <br />
<br />
|- <br />
|| 10:43<br />
|| Let's summarize. <br />
<br />
|- <br />
|| 10:45<br />
|| In this tutorial, we have learnt, <br />
<br />
How to draw a '''vector''' <br />
<br />
|- <br />
|| 10:49<br />
|| Arithmetic operations on '''vectors''' <br />
<br />
|- <br />
|| 10:52<br />
|| How to create a '''matrix''' <br />
<br />
|- <br />
|| 10:54<br />
|| Arithmetic operations on '''matrices''' <br />
<br />
|- <br />
|| 10:58<br />
|| '''Transpose''' of a '''matrix''' <br />
<br />
|- <br />
|| 11:01<br />
|| '''Determinant''' of a '''matrix''' <br />
<br />
|- <br />
|| 11:04<br />
|| '''Inverse''' of a '''matrix''' .<br />
<br />
|- <br />
||11:06<br />
|| The video at the following link summarises the Spoken Tutorial project. <br />
<br />
Please download and watch it. <br />
<br />
|- <br />
|| 11:14<br />
|| The '''Spoken Tutorial Project ''' team: <br />
<br />
conducts workshops using spoken tutorials and gives certificates on passing online tests. <br />
<br />
|- <br />
|| 11:22<br />
|| For more details, please write to us. <br />
<br />
|- <br />
|| 11:25<br />
|| Do you have questions in THIS Spoken Tutorial? <br />
<br />
Please visit this site <br />
<br />
|- <br />
|| 11:30<br />
|| Choose the minute and second where you have the question <br />
<br />
|- <br />
|| 11:34<br />
|| Explain your question briefly <br />
<br />
|- <br />
|| 11:37<br />
|| Someone from our team will answer them.<br />
<br />
|- <br />
|| 11:40<br />
|| The Spoken Tutorial forum is for specific questions on this tutorial <br />
<br />
|- <br />
|| 11:45<br />
|| Please do not post unrelated and general questions on them <br />
<br />
This will help reduce the clutter <br />
<br />
|- <br />
|| 11:52<br />
|| With less clutter, we can use these discussion as instructional material. <br />
<br />
|- <br />
|| 11:57<br />
|| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. <br />
<br />
|- <br />
|| 12:03<br />
|| More information on this mission is available at this link. <br />
<br />
|- <br />
|| 12:08<br />
|| This is Madhuri Ganapathi from, IIT Bombay signing off. <br />
<br />
Thank you for watching. <br />
|-<br />
|}</div>PoojaMoolya