CHAPTER 01.04: INTRODUCTION: What is a submatrix?

In this segment, we will talk about what is a sub-matrix. So given matrix A, take out rows; you can take out rows and/or columns; you are left with a sub-matrix. So a matrix will have many sub-matrices.

So it is very clear from example, somebody says “Hey I’m going to find some of the sub-matrices” - I’m not going to show all the sub-matrices. So somebody says “Hey, 2, 3, 6, 7, 8, 9, 6, 3, 4, 9, 10 and 13 - and I’m going to find all the sub-matrices of A.” I’m just going to show you a few of them. You can do some of them at home. So for example, if I get rid of the 1st row, then what am I left with? I’m left with a sub-matrix, which has the other 3 rows in it: 7, 8, 9, 6, 3, 4, 9, 10 and 13. So that is a sub-matrix.

Somebody says “Hey, get rid of the first column.” Then my sub-matrix here C of A would be 3, 6, 8, 9, 3, 4, 10 and 13 - like that. But as I said, you don’t have to take out just one row or one column or one row and one column. You can take out as many rows and as many columns out. For example, somebody says “Hey, what I want you to do is I want you to take the first row out and the first 2 columns out.” So somebody says “Hey go ahead and take out the first row and the first two columns,” you are only left with this part right here. So the sub-matrix for taking the 1st two columns out and the first row out would be 9, 4 and 13. So that is how we find sub-matrices of a matrix. These are important concepts which you will have to use when we talk about a system of equations. And that is the end of this segment.