Difference between revisions of "LibreOffice-Suite-Math-6.3/C2/Matrices-and-Aligning-equations/English"

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−
'''Keywords: Libreoffice Math, Libreoffice Writer, Matrices, equations, align, format, addition, equations, multiplication, video tutorial'''.
+
'''Keywords: Libreoffice Math, Libreoffice Writer, Matrices, equations, align, format, addition, equations, multiplication, spoken tutorial, video tutorial'''.
  
  
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|| '''Slide:Title Slide'''
 
|| '''Slide:Title Slide'''
−
|| Welcome to the spoken tutorial on '''Matrices and Aligning Equations.'''
+
|| Welcome to this spoken tutorial on '''Matrices and Aligning Equations'''.
 
|-  
 
|-  
 
|| '''Slide''':
 
|| '''Slide''':
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|| In this tutorial, we will learn how to:
 
|| In this tutorial, we will learn how to:
 
* Write a '''matrix'''
 
* Write a '''matrix'''
−
* '''Format '''the '''matrices.'''
+
* '''Format '''the '''matrices'''
 
* '''Align '''the '''equations'''  
 
* '''Align '''the '''equations'''  
 
|-  
 
|-  
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'''Code Files'''
 
'''Code Files'''
 
||  
 
||  
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* The files used in this tutorial are provided in the''' Code files''' link.  
+
* The files used in this tutorial are provided in the ''' Code files''' link.  
 
* Please download and extract the files.
 
* Please download and extract the files.
 
* Make a copy and use them for practising.
 
* Make a copy and use them for practising.
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|-  
 
|-  
 
|| Open the '''MathExample1.odt '''
 
|| Open the '''MathExample1.odt '''
−
|| Let us first open the '''MathExample1.odt '''file.
+
|| Let us first open the '''MathExample1.odt ''' file.
 
|-  
 
|-  
 
|| '''Pause '''in each page for a few seconds.  
 
|| '''Pause '''in each page for a few seconds.  
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Press '''Ctrl + Enter,''' to go to a new page.
 
Press '''Ctrl + Enter,''' to go to a new page.
−
|| Notice all the previous example '''formulae '''which we had written using '''Math'''.
+
|| Notice all the previous example '''formulae ''' which we had written using '''Math'''.
  
  
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'''Insert''' menu and select '''Object.'''
+
Click on the '''Insert''' menu and select '''Object'''.
  
−
From the submenu, select '''Formula''' option.
+
From the sub-menu, select '''Formula''' option.
 
|-
 
|-
 
||Click on '''Format''' >> Select '''Font size'''.
 
||Click on '''Format''' >> Select '''Font size'''.
Line 98: Line 98:
  
  
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|| Let us now see what''' matrix''' is?
+
|| Let us now see what ''' matrix''' is?
  
 
'''Matrix ''' is a rectangular '''array '''of numbers or symbols, called '''elements'''.
 
'''Matrix ''' is a rectangular '''array '''of numbers or symbols, called '''elements'''.
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−
Here we have used the '''matrix markup'''.
+
We have used the '''matrix markup'''.
  
 
We have included its '''elements''' in curly brackets.
 
We have included its '''elements''' in curly brackets.
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−
'''Parentheses '''are used to enclose the elements of a '''matrix'''.
+
'''Parentheses ''' are used to enclose the elements of a '''matrix'''.
 
|-  
 
|-  
 
|| Point to the '''Parentheses.'''
 
|| Point to the '''Parentheses.'''
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|| Notice that the '''parentheses ''' are short.
 
|| Notice that the '''parentheses ''' are short.
  
−
They do not enclose all the '''elements '''of the '''matrix'''.
+
They do not enclose all the '''elements ''' of the '''matrix'''.
  
  
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−
Hence are not ''' scalable''' to the size of the '''matrix'''.
+
Hence they are not ''' scalable''' to the size of the '''matrix'''.
 
|-
 
|-
 
||Point to the '''elements''' and parentheses.
 
||Point to the '''elements''' and parentheses.
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|-
 
|-
 
||Point to the '''Writer''' gray box
 
||Point to the '''Writer''' gray box
−
||Notice that '''parentheses''' have enclosed all the '''elements'''.
+
||Notice that '''parentheses''' have now enclosed all the '''elements'''.
 
|-
 
|-
 
||'''Highlight in Formula Editor'''.
 
||'''Highlight in Formula Editor'''.
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−
The '''markup''' for a '''4 by 1 matrix''' '''matrix '''is shown in the '''formula editor'''.
+
The '''markup''' for a '''4 by 1 matrix''' is shown in the '''formula editor'''.
  
  
−
This is a '''4 by 1 matrix''' in the''' preview '''area.
+
This is a '''4 by 1 matrix''' in the''' preview ''' area.
 
|-
 
|-
 
||Point to the '''Writer''' gray box
 
||Point to the '''Writer''' gray box
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In '''Formula Editor Window''', Point mouse over last line.
 
In '''Formula Editor Window''', Point mouse over last line.
−
||Here we can also use''' square brackets''' instead of '''parentheses'''.
+
||Here we can also use ''' square brackets''' instead of '''parentheses'''.
  
  
−
We can write '''matrices '''of any dimension using the '''matrix markup'''.
+
We can write '''matrices ''' of any dimension using the '''matrix markup'''.
 
|-  
 
|-  
 
|| '''Highlight in Formula editor.'''
 
|| '''Highlight in Formula editor.'''
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Press '''Enter''' twice
 
Press '''Enter''' twice
−
|| Now let us write an example for '''matrix addition.'''
+
|| Let us now write an example for '''matrix addition.'''
  
  
−
Press the '''Enter '''key twice to add two blank lines.
+
Press the '''Enter ''' key twice to add two blank lines.
 
|-
 
|-
 
||Copy and paste:
 
||Copy and paste:
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−
Click between the two '''matrices '''and add a plus sign with a '''blank format'''.
+
Click between the two '''matrices ''' and add a plus sign with a '''blank format'''.
  
  
 
|-  
 
|-  
 
|| Type''' ~=~ '''at the end of the last line.
 
|| Type''' ~=~ '''at the end of the last line.
−
|| Next let us add an ‘'''equal to'''’ symbol at the end with a '''blank format. '''
+
|| Next let us add an ‘'''equal to'''’ symbol at the end with a '''blank format'''.
 
|-  
 
|-  
 
|| Copy and paste at the end:
 
|| Copy and paste at the end:
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|-  
 
|-  
 
|| Click '''Save icon '''on '''Standard ''' toolbar.
 
|| Click '''Save icon '''on '''Standard ''' toolbar.
−
|| Let us save the file now.
+
|| Let us now save the file.
 
|-  
 
|-  
 
|| Copy and paste:
 
|| Copy and paste:
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'''4 times Left( matrix {%alpha # %beta # %gamma ## %theta # %eta # %mu } Right) '''
 
'''4 times Left( matrix {%alpha # %beta # %gamma ## %theta # %eta # %mu } Right) '''
−
|| Next, let us see an example of multiplying a '''matrix '''with a number.
+
|| Next, let us see an example of multiplying a '''matrix ''' with a number.
  
  
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|-  
 
|-  
 
|| Type''' ~=~''' at the end.
 
|| Type''' ~=~''' at the end.
−
|| Let us write the ‘'''equal to'''’ symbol at the end with a '''blank space.'''
+
|| Let us write the ‘'''equal to'''’ symbol at the end with a '''blank space'''.
 
|-  
 
|-  
 
|| Copy and paste at the end:
 
|| Copy and paste at the end:
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−
'''Click '''on the '''Format '''menu.  
+
'''Click '''on the '''Format ''' menu.  
  
  
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|| Pause the video and do this assignment.
 
|| Pause the video and do this assignment.
  
−
* Open '''Math-assignment.odt '''file.
+
* Open '''Math-assignment.odt ''' file.
−
* Write steps to multiply a '''2x3 matrix''' by a''' 3x1 matrix'''.  
+
* Write steps to multiply a '''2x3 matrix''' by a ''' 3x1 matrix'''.  
−
* Use formatting options to change the '''fonts''', '''font sizes '''and '''spacing'''.
+
* Use formatting options to change the '''fonts''', '''font sizes ''' and '''spacing'''.
  
 
|-  
 
|-  
 
|| Only narration
 
|| Only narration
−
|| Now, we will use '''matrices '''to write '''simultaneous '''equations and '''align '''them.
+
|| Now, we will use '''matrices ''' to write '''simultaneous ''' equations and '''align ''' them.
  
 
|-
 
|-
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−
'''Insert''' menu and select '''Object.'''
+
Click on the '''Insert''' menu and select '''Object'''.
  
 
From the submenu, select '''Formula'''.
 
From the submenu, select '''Formula'''.
Line 389: Line 389:
 
'''x+y=6 newline newline'''
 
'''x+y=6 newline newline'''
  
−
|| Let us now write a set of '''Simultaneous '''equations as shown on the screen.
+
|| Let us now write a set of '''Simultaneous ''' equations as shown on the screen.
  
  
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Point mouse over '''2x''', point over '''y''', point over '''<nowiki>=</nowiki>'''.
 
Point mouse over '''2x''', point over '''y''', point over '''<nowiki>=</nowiki>'''.
  
−
|| Notice that they are not '''aligned '''at the '''plus sign '''and''' equal to '''character.
+
|| Notice that they are not '''aligned '''at the '''plus sign '''and''' equal to ''' character.
  
  
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−
Here alignment at the '''plus sign '''and''' equal to sign '''is done using the curly brackets.
+
Here alignment at the '''plus sign ''' and ''' equal to sign ''' is done using the curly brackets.
  
 
Also note that a '''hash ''' symbol is used to separate each element of this equation.
 
Also note that a '''hash ''' symbol is used to separate each element of this equation.
  
 
   
 
   
−
We have used two ''' hash '''symbols to separate the equations.
+
We have used two ''' hash ''' symbols to separate the equations.
 
|-
 
|-
 
||In the '''Writer''' gray box
 
||In the '''Writer''' gray box
−
||This is a perfectly '''aligned '''set of equations.
+
||This is a perfectly '''aligned ''' set of equations.
 
|-  
 
|-  
 
|| In '''Formula Editor''' Window,, press '''Enter''' twice, copy and paste:
 
|| In '''Formula Editor''' Window,, press '''Enter''' twice, copy and paste:
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−
Notice the equations''' '''on the screen.
+
Notice the equations on the screen.
  
  
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|-  
 
|-  
 
|| Point to the equatios.
 
|| Point to the equatios.
−
|| Here we have used '''alignr '''and '''alignl '''to align the parts.  
+
|| Here we have used '''alignr ''' and '''alignl ''' to align the parts.  
  
  
−
Note that the set of equations is '''aligned '''to right and left of the '''equal to''' sign.
+
Note that the set of equations are '''aligned ''' to right and left of the '''equal to''' sign.
  
 
|-  
 
|-  
 
|| '''Ctrl + S'''
 
|| '''Ctrl + S'''
−
|| Let us save the changes.
+
|| Let us now save the changes.
 
|-  
 
|-  
 
|| Narration only:
 
|| Narration only:
−
|| With this we have come to the end of this tutorial.
+
|| With this we come to the end of this tutorial.
  
  
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|| In this tutorial we have learnt how to:
 
|| In this tutorial we have learnt how to:
 
* Write a '''matrix'''
 
* Write a '''matrix'''
−
* '''Format ''' the '''matrices.'''
+
* '''Format ''' the '''matrices''' and
 
* '''Align '''the '''equations'''  
 
* '''Align '''the '''equations'''  
  
Line 512: Line 512:
 
* Open '''Math-assignment.odt ''' file.
 
* Open '''Math-assignment.odt ''' file.
 
* Write a set of three equations.  
 
* Write a set of three equations.  
−
* Align the '''equations''' at the plus or minus signs and '''equal to '''character.
+
* Align the '''equations''' at the plus or minus signs and '''equal to ''' character.
  
 
|-  
 
|-  
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||  
 
||  
−
* We conduct workshops using '''spoken''' '''tutorials''' and give certificates.
+
* We conduct workshops using '''spoken tutorials''' and give certificates.
 
* For more details, please contact us.
 
* For more details, please contact us.
  
Line 540: Line 540:
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
−
||The''' Spoken''' '''Tutorial''' project is funded by the M'''inistry of Education''', Govt. of India.
+
||The''' Spoken''' '''Tutorial''' project is funded by the '''Ministry of Education''', Govt. of India.
 
|-  
 
|-  
 
|| '''Slide: Thank you'''
 
|| '''Slide: Thank you'''
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|| This tutorial was originally contributed by DesiCrew Solutions Pvt. Ltd. in 2011
 
|| This tutorial was originally contributed by DesiCrew Solutions Pvt. Ltd. in 2011
  
−
This is Madhuri Ganapathi along with the Spoken Tutorial team from '''IIT Bombay.'''
+
This is Madhuri Ganapathi along with the Spoken Tutorial team from '''IIT Bombay'''.
  
 
Thank you for watching.
 
Thank you for watching.
 
|-
 
|-
 
|}
 
|}

Revision as of 14:41, 1 September 2022

Title: Matrices and Aligning Equations


Keywords: Libreoffice Math, Libreoffice Writer, Matrices, equations, align, format, addition, equations, multiplication, spoken tutorial, video tutorial.


Visual Cue Narration
Slide:Title Slide Welcome to this spoken tutorial on Matrices and Aligning Equations.
Slide:

Learning Objectives

In this tutorial, we will learn how to:
  • Write a matrix
  • Format the matrices
  • Align the equations
Slide:

System Requirements

This tutorial is recorded using:
  • Ubuntu Linux OS version 18.04 and
  • LibreOffice Suite version 6.3.5
Slide:

Prerequisites

https:\\spoken-tutorial.org

To follow this tutorial, learner should be familiar with Math interface.


If not please access the relevant tutorials on this website.

Slide:

Code Files

  • The files used in this tutorial are provided in the Code files link.
  • Please download and extract the files.
  • Make a copy and use them for practising.
Open the MathExample1.odt Let us first open the MathExample1.odt file.
Pause in each page for a few seconds.

Scroll to the next page and repeat.


Press Ctrl + Enter, to go to a new page.

Notice all the previous example formulae which we had written using Math.


Press Ctrl and Enter, keys to go to a new page.

Type Matrices and Aligning Equations On the new page, type Matrices and Aligning Equations.


Insert menu >> select Object.

From the submenu >> select Formula option.


Now let us call the Math application inside Writer.


Click on the Insert menu and select Object.

From the sub-menu, select Formula option.

Click on Format >> Select Font size.

In the Font sizes dialog box change the Base Size to 18 pt.

Click OK button

Click on Format >> Select Alignment >>

Click Left option. Click OK button

Let us change the font size to 18 point and alignment to Left.
Slide:

Matrix


Let us now see what matrix is?

Matrix is a rectangular array of numbers or symbols, called elements.


Math has a separate markup to represent a matrix.

Show the text editor with examples. I have written a few examples of matrices in a text editor.

I will copy and paste them to save time.

Highlight in Formula Editor.


Copy and paste:

"Example of a 2x3 Matrix:" newline newline

A ~=~ ( matrix {a # b # c ## d # e# f } ) newline newline

This is a matrix markup for a 2 by 3 matrix.
Highlight in Formula Editor.

Point mouse over matrix word.


Point mouse over individual # symbol


Point mouse over ## symbols.


Point mouse over ( and ).


Point mouse over ( and ) in Writer gray box

This matrix has 2 rows and 3 columns.


We have used the matrix markup.

We have included its elements in curly brackets.


Elements are separated using a hash symbol.


Rows in the matrix are separated using two hash symbols.


Parentheses are used to enclose the elements of a matrix.

Point to the Parentheses.

Point to the elements.


Notice that the parentheses are short.

They do not enclose all the elements of the matrix.


Parentheses are of the same size as each element.


Hence they are not scalable to the size of the matrix.

Point to the elements and parentheses.

Type Left just before ( character and Right before ) character in the formula

To make the parentheses scalable, we will use Left and Right keywords.


Type Left before the opening parenthesis.

Type Right before closing the parenthesis.

Point to the Writer gray box Notice that parentheses have now enclosed all the elements.
Highlight in Formula Editor.


Copy and paste

"Example of 4x1 Matrix: " newline newline

B ~=~ Left ( matrix {1##2##3##4} Right ) newline newline


Point mouse over ( and )

Next we will see another example matrix.


The markup for a 4 by 1 matrix is shown in the formula editor.


This is a 4 by 1 matrix in the preview area.

Point to the Writer gray box Notice that parentheses have enclosed all the elements.
Change () to [ ]

B ~=~ Left [ matrix {1##2##3##4} Right ] newline newline


In Formula Editor Window, Point mouse over last line.

Here we can also use square brackets instead of parentheses.


We can write matrices of any dimension using the matrix markup.

Highlight in Formula editor.


Press Enter twice

Let us now write an example for matrix addition.


Press the Enter key twice to add two blank lines.

Copy and paste:

"Example of 2x3 Matrix Addition:" newline newline

Left( matrix {a # b # c ## d # e# f } Right)

Left( matrix {%alpha # %beta # %gamma ## %theta # %eta # %mu } Right)

Let us write two 2 by 3 matrices one beside the other as shown on the screen.


Click in between the gap of these two matrices.


Point mouse over the cursor in the FEW.

Type ~+~ in between these two matrices


Next, let us add a plus sign in between the two matrices to denote addition.


Click between the two matrices and add a plus sign with a blank format.


Type ~=~ at the end of the last line. Next let us add an ‘equal to’ symbol at the end with a blank format.
Copy and paste at the end:

Left( matrix {a+%alpha # b+%beta # c+%gamma ## d+%theta # e+%eta # f+%mu } Right) newline newline


Point mouse over the last formula in the Writer gray box.

The third matrix on the right denotes the addition.


Notice that we have used Greek characters in our example.

Click Save icon on Standard toolbar. Let us now save the file.
Copy and paste:

"Example of Matrix Multiplication with a number: " newline newline

4 times Left( matrix {%alpha # %beta # %gamma ## %theta # %eta # %mu } Right)

Next, let us see an example of multiplying a matrix with a number.


This is a 2 by 3 matrix multiplied by 4.


We have written 4 times followed by the matrix.

Type ~=~ at the end. Let us write the ‘equal to’ symbol at the end with a blank space.
Copy and paste at the end:

Left( matrix {4%alpha # 4%beta # 4%gamma ## 4%theta # 4%eta # 4%mu } Right) newline newline newline


Point mouse over the last formula in Writer gray box

This is the markup for the matrix product.


This is the product of multiplying a 2 by 3 matrix with a number.

Click on Format, and point on the sub menu slowly one by one. Now, we will format the matrices.


Click on the Format menu.


We can choose Fonts, Font Sizes, Spacing or Alignment options for formatting.

Click on the Spacing option.


Default sizes:

Line Spacing field 3%

Column spacing field 30%


Point to the dialog box.

Let us choose the Spacing option.

Spacing dialog box opens.

Click on the Category drop down at the bottom, and choose Matrices

Change Line spacing to 20%, Column spacing to 40%


Click on the OK button.


Point mouse over Writer gray box.

In the Category drop down, let us choose Matrices.


Let’s change the Line spacing to 20 percent and Column spacing to 40 percent.


Click on the OK button in the dialog box.

Point in the Writer gray box Notice that the matrices and their elements are properly spaced.
Slide:

Assignment

Pause the video and do this assignment.
  • Open Math-assignment.odt file.
  • Write steps to multiply a 2x3 matrix by a 3x1 matrix.
  • Use formatting options to change the fonts, font sizes and spacing.
Only narration Now, we will use matrices to write simultaneous equations and align them.
Press Ctrl and Enter keys. Press Ctrl and Enter keys to go to a new page.
Insert menu >> select Object.

From the submenu >> select Formula option.


Let us open the Math application.


Click on the Insert menu and select Object.

From the submenu, select Formula.

Click on Format >> Select Font size.

In the Font sizes dialog box change the Base Size to 18 pt.

Click OK button

Let us change the font size to 18 point.
In Formula Editor Window, press Enter, key twice,

Copy and paste:

"Simultaneous Equations: " newline newline

2x+y = 8 newline

x+y=6 newline newline

Let us now write a set of Simultaneous equations as shown on the screen.


Point mouse over the last formula Write Gray box


Point mouse over 2x, point over y, point over =.

Notice that they are not aligned at the plus sign and equal to character.


We can use the matrix markup to align them.


We can separate each part of the equation and treat it as element of a matrix.


Here, 2x, y, plus sign and equal to are different parts of the equation.

In Formula Editor Window, Press Enter, twice, copy and paste:

matrix { 2x # {}+{} # y # {}={} # 8 ## x # {}+{} # y # {}={} # 6 }


Point to the curly brackets.


Point mouse over # symbols


Point mouse over ## symbol


Press Enter key.


This is a new set of matrix markup.


Here alignment at the plus sign and equal to sign is done using the curly brackets.

Also note that a hash symbol is used to separate each element of this equation.


We have used two hash symbols to separate the equations.

In the Writer gray box This is a perfectly aligned set of equations.
In Formula Editor Window,, press Enter twice, copy and paste:

newline newline

x+y=2 newline

x=2-y newline newline


Point mouse over last formula in the Writer gray box

Let us write another set of equations.


Notice the equations on the screen.


Note that LHS ad RHS do not have equal number of parts.


Hence they are not aligned at the plus sign, minus sign and equal to sign.


In Formula editor window, press Enter, twice, copy and paste:

matrix{ alignr x+y # {}={} # alignl 2 ## alignr x # {}={} # alignl 2-y }


In Formula editor window, point mouse over alignr and alignl and the ‘=’ character.


Point mouse over the last formula Write Gray box

Let us write the matrix markup to align them.


Point to the equatios. Here we have used alignr and alignl to align the parts.


Note that the set of equations are aligned to right and left of the equal to sign.

Ctrl + S Let us now save the changes.
Narration only: With this we come to the end of this tutorial.


Let us summarize.

Slide:

Summary

In this tutorial we have learnt how to:
  • Write a matrix
  • Format the matrices and
  • Align the equations
Slide:

Assignment

Here is an assignment for you:
  • Open Math-assignment.odt file.
  • Write a set of three equations.
  • Align the equations at the plus or minus signs and equal to character.
Slide:

About Spoken Tutorial Project

  • The video at the following link summarises the Spoken Tutorial project.
  • Please download and watch it.
Slide:

Spoken tutorial workshops

  • We conduct workshops using spoken tutorials and give certificates.
  • For more details, please contact us.
Slide:

Answers for THIS Spoken Tutorial

Please post your Timed queries in this forum.
Slide:

Acknowledgement

The Spoken Tutorial project is funded by the Ministry of Education, Govt. of India.
Slide: Thank you

Acknowledgement to DesiCrew

This tutorial was originally contributed by DesiCrew Solutions Pvt. Ltd. in 2011

This is Madhuri Ganapathi along with the Spoken Tutorial team from IIT Bombay.

Thank you for watching.

Contributors and Content Editors

Madhurig, Nancyvarkey, Nirmala Venkat

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