View source for LibreOffice-Suite-Math-6.3/C2/Matrices-and-Aligning-equations/English

'''Title: Matrices and Aligning Equations'''


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



{| border=1
|| '''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'''


|| Now let us now see what a''' 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'''.


This '''matrix '''has''' 2 rows''' and '''3 columns.'''
|- 
|| '''Highlight in Formula Editor'''.

Point mouse over '''matrix ''' word.


Point mouse over individual '''<nowiki># </nowiki>'''symbol


Point mouse over '''<nowiki>##</nowiki>''' symbols.


Point mouse over '''(''' and ''')'''.


Point mouse over '''( '''and ''') ''' in '''Writer ''' gray box
||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 '''<nowiki>=</nowiki>'''.

|| 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.

|-
||Press '''Enter'''
|| Press '''Enter''' key. 
|- 
|| 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 '''<nowiki># </nowiki>''' symbols


Point mouse over '''<nowiki>## </nowiki>''' symbol

||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.
|-
||
|| Let us write another 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

||Notice the equations on the screen.


Note that LHS ad RHS do not show 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 ‘'''<nowiki>=</nowiki>'''’ 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.
|-
|}