00:01
Okay, so in this question, we're asked to find the inverse and verify that b, b, inverse, equals b inverse b equals the identity matrix.
00:09
So first we're going to begin by finding the inverse of this 3x3 matrix that we have.
00:16
So for 3 by 3 matrices, the first step is you want to put the original matrix right here on the left.
00:22
We'll align and then put the identity matrix on the right side.
00:27
Here we have i3 because we're dealing with the 3x3 matrix.
00:31
And the goal is to get the left side to look like the identity matrix.
00:36
And after doing all of those row operations, to get the left side to look like the identity matrix, the right side will then be our inverse matrix.
00:44
So first we're going to do row 3 plus 2 r1, and what that does is turn this negative 2 into a 0.
00:51
So in the third row, we end up getting 0, 5, 4, 201.
00:57
Then next we're going to do row 2 divided by 2, and that, turns this 2 into a 1.
01:03
And so in row 2, we get 0 -1 -1 -0, 1 -5 -0.
01:10
Then next we're going to do row 3 minus 5, row 2.
01:14
And we do this so that this 5 turns into a 0.
01:18
And so in row 3 we end up getting 0, 0, negative 1, 2, negative 5 over 2, 1.
01:26
And then we're going to do row 2 plus row 3.
01:30
And this turns this 1 into a 0.
01:32
And we can already see that we're very close to getting the identity matrix on the left side.
01:38
So in row 2, we get 0, 1, 0 ,0, 2, negative 2, 1.
01:44
And then we can do row 3 times negative 1...