00:01
Okay, so for this problem, we are asked to find the determinant of this matrix, and when we're dealing with determinants and matrices that are over 2 by 2, maybe even 3 by 3, the equation for finding the determinant becomes a little funky.
00:17
So something to remember is that we want to work with triangular matrices.
00:23
And so let me give you an example of what that is.
00:27
So we could have 1, 2, 3, 2, 2, 3, 2, 3, 2.
00:30
3, 3, then 0 ,000.
00:33
And so all of these on my diagonal have a value, but then everything else is underneath is zeros.
00:44
And so in order to do the determinant of this, you would just take our determinant of, we'll call this b, would be equal to 1 times 2 times 3, which is equal to 6.
01:00
So i'm just multiplying all of these diagonals together.
01:04
So that makes finding the determinant really, really easy when we're dealing with triangular matrices.
01:11
So that's exactly what we're going to want to make this matrix into.
01:16
So first up, i'm just going to switch around some rows.
01:20
So i'm going to take row one and move it to row three.
01:27
And then i'm going to take row two and move that to row one, row three, move that to row five.
01:40
And then row four, i'm going to move that to row two, row five is going to get moved to row three, four.
01:55
And so that's going to yield me with a matrix looking like this one...