CHAPTER 01.01: INTRODUCTION: What is a matrix?

What is a matrix? A matrix is a rectangular array of elements. So let’s suppose we have an A matrix here and we will write down the A elements. A 1 1, A 1 2 all the way up to A 1 N. Then we can have A 1 M here and all the way up to A M N here. What this means is that we have order of the matrix. The order of the matrix is how many rows does it have and how many columns it has. So that is M by N. So M rows and N columns. That is called the order of the matrix.

So then each of these which are seen here are these entries that are called entry or element. But what you are finding out is that each of these entries or elements has a position notated with them. So you have A 1 2 here. For example, that means that it is in the 1st row and is in the 2nd column. So every entry you will have 2 subscripts, I and J, where the I will correspond to the row number and the J will correspond with the column number.

So let’s look at an example here. Let’s suppose somebody says, “Hey, my A matrix looks like this: 20, 3, 6, 7, 8, -19.” So if that’s what the A matrix looks like, we will have 2 rows and 3 columns; because we have one row, two row and then we have 3 columns: 1, 2, and 3 - 3 columns-. So for each of these column entries, let’s suppose we look at this particular entry right here. This one is in the 1st row and it is in the 3rd column, so it is A 1 3. So I can say A 1 3 is equal to 6, for example. So, that is how we denote each of the terms that are in the A matrix. And that is the end of this segment.