LibreOffice-Suite-Math/C2/Matrices-Aligning-Equations/English-timed

Time	Narration
00:00	Welcome to the Spoken tutorial on LibreOffice Math.
00:04	In this tutorial, we will learn how to: * Write a matrix and
00:08	* Align equations on a particular character.
00:12	For this, let us first open our example Writer document that we created in our previous tutorials- "MathExample1.odt".
00:25	Notice all the previous example formulae which we wrote using Math.
00:30	Now, let us scroll to the last page of the document and press Control, Enter to go to a new page.
00:39	Let us call Math by clicking Insert menu, then Object and then Formula.
0049:	In mathematics, a matrix is a rectangular array of numbers or symbols which are called elements.
00:59	'Math' has separate mark up to represent a matrix and its rows and columns of elements.
01:08	I have the examples written already so as to save time. I will copy and paste them. Now, we’ll learn how to write a 2 by 3 matrix.
01:24	This matrix has 2 rows and 3 columns.
01:29	We will use the markup matrix and include all its elements within curly brackets, in the Formula Editor window.
01:40	Notice that the elements in a row are separated by one hash symbol
01:48	and the rows are separated by two hash symbols.
01:55	Use parentheses to enclose the matrix in brackets.
02:01	Now, notice that the brackets are short and do not cover all the elements in the matrix entirely.
02:12	They are of the same size as each element and hence are not scalable to the size of the matrix.
02:22	To solve this, we can use the words ‘Left’ and ‘Right’.
02:28	i.e. 'Left', just before open bracket and 'Right', before close bracket to make the brackets scalable.
02:41	Let me copy and paste the next example.
02:46	So, a 4 by 1 matrix will look like as shown on the screen.
02:52	Notice the scalable brackets in the Writer gray box.
02:57	The markup for the matrix is as shown on the screen.
03:03	Here, we can also use square brackets instead of parentheses.
03:09	So, using the matrix mark up, we can write matrices of any dimensions.
03:17	Now, let us write an example for matrix addition.
03:23	Let us go to a new line in the Formula Editor window.
03:28	We can press the Enter key twice to add two blank lines.
03:36	First, let us write two example 2 by 3 matrices, side by side, as shown on the screen.
03:46	Next, let us add a plus symbol in between these two matrices to denote addition.
03:54	To do this, we can simply click between the gap of these two matrices in the Writer Gray box.
04:03	Notice that the cursor in the Formula Editor Window is placed roughly between the two matrix mark ups here.
04:12	Type plus (+) in between these two matrices.
04:17	So, there is the plus symbol (+).
04:20	Next, let us add an equal to symbol (=) at the end with long gaps.
04:28	And then, the third matrix on the right, denoting the addition.
04:35	Notice that we have used Greek characters in our example.
04:42	So, there is the result of the addition of two matrices.
04:47	Let us save our work.
04:50	Next, let us see an example of multiplying a matrix by a number.
04:58	We will write a 2 by 3 matrix and multiply it by 4.
05:04	We will first write 4 times, followed by the matrix.
05:10	Let me copy the matrix and paste it in FEW.
05:17	Next, let us write the equal to (=) symbol at the end with long gaps
05:24	followed by the matrix product. I am copying and pasting the mark up for the matrix product.
05:33	So, there is the product of multiplying a 2 by 3 matrix by a number.
05:40	Now, we can format matrices by clicking on the Format menu and choosing the Fonts, Font Size, Alignment or the Spacing.
05:51	For example, let us choose Spacing.
05:55	In the Category drop-down, on the right, let us choose Matrices
06:02	and change the Line spacing to 20 percent and column spacing to 50 percent. Click OK.
06:17	Notice, how the matrices and their elements are well spaced out.
06:23	Let us save our work now by clicking on File and Save.
06:29	Now, we can also use matrices to write two or three equations and then align them on a particular character.
06:37	For example, we can write simultaneous equations and align them on the equal to character.
06:46	Let us write a set of simultaneous equations now, as shown on the screen.
06:52	Notice that they are not perfectly aligned on the equal to character.
06:58	So, here we can use the matrix mark-up to align them.
07:03	We can separate each part in the equation and treat the parts as elements of a matrix.
07:10	Here, '2x' is a part, 'y' is a part, equal to character is a part and so on.
07:20	Press Enter twice. Copy and paste the mark up.
07:26	And, thus the new mark up looks like as shown on the screen.
07:31	Here, we have used the matrix mark up, treated each part of the equation as an element and separated them by # (hash) symbols.
07:43	We have used the double hash symbols to separate the two equations.
07:50	So, there is a perfectly aligned set of equations.
07:56	Let us write another set of equations.
07:59	Here, let us suppose that we don’t have equal number of parts on the left and the right of the equal to character.
08:09	Notice the equations on the screen and they are not aligned on the equal to character.
08:16	Let us rewrite the mark up to align them. Press Enter twice. I am copying and pasting the markup.
08:25	So here, we have used alignr and alignl to align the parts to the right and the left of the equal to character.
08:36	And, there is our perfectly aligned set of equations.
08:41	Here is an assignment for you:
08:43	Write steps for multiplying a 2x3 matrix by a 3x1 matrix. Use formatting to change the font sizes and the spacing.
08:56	Write a set of three equations. Align the equations at the equal to (=) character.
09:04	This brings us to the end of this tutorial on Matrix and Aligning equations in LibreOffice Math.
09:11	To summarize, we learned the following topics:
09:15	* Write a Matrix and * Align equations on a particular character.
09:20	Spoken Tutorial project is a part of the Talk to a Teacher project, supported by the National Mission on Education through ICT, MHRD, Government of India.
09:32	This project is coordinated by http://spoken-tutorial.org.
09:37	More information on the same is available at the following link.
09:40	This script has been contributed by Priya Suresh, DesiCrew Solutions. And this is Soundharya, DesiCrew Solutions, signing off. Thanks for joining.

Contributors and Content Editors

Minal, PoojaMoolya, Pratik kamble, Sandhya.np14