00:04
So we start out with a matrix that has k1, k2, k3, k4 along the diagonal.
00:11
Each k is a non -zero real number.
00:15
And then also this matrix is going to have just zeros everywhere else.
00:25
The inverse matrix is going to essentially just cancel out the diagonal and get ones.
00:31
So we're going to do the reciprocal for each k to do that.
00:34
So we'll have 1 over k1, 0, 0, 0, 0.
00:41
1 over k2, 0, 0, 0, 0, 0.
00:47
1 over k3, 0.
00:50
Then 0, 0, 0, and 1 over k4.
00:59
So that's your inverse for the first matrix.
01:03
The other matrix we're given k0, 0, 0, 1, 1, 0, 0, 0, 0, k0, 0, 0, 1, 1.
01:18
K again is a non -zero real number.
01:23
To figure this out, i'm going to put the identity matrix after it.
01:37
And then i want to do row operations to where the left side of this is going to be the identity.
01:44
And then that's going to make the right -hand side equal to the inverse.
01:49
So if i want to get the identity matrix on the left side, what i got to first do is try to make this k equal to 1, and then this 1 equal to 0.
02:08
To get my 0, i'm going to do negative row 2 plus row 1 and put it in row 1.
02:18
So let's work out what we would have...