00:01
So this question we have e1, e2, e3 are the standard basis, and we have w1 is 1, 3, 2, w2 is 0, 3, 2, and w3 is 1, 4, 3 are a new basis.
00:25
And we want to find the change of basis from e1, e2, e3 to w1, w2, w3.
00:33
So the change of basis matrix m takes e1, e2, e3 to w1, w2, w3, but it's a change of basis.
00:41
It's going to be the inverse of just the matrix made out of these columns.
00:57
So first of all, let's write m to the power of minus 1 is 1, 3, 2, 0, 3, 2, 1, 4, 3.
01:09
Let's find the determinant.
01:15
We get 1 times the determinant of 3, 4, 2, 3 minus 0 times the determinant of 3, 2, 4, 3 plus 1 times the determinant 3, 3, 2, 2.
01:30
So that's 9 minus 8 is 1.
01:34
And here this is 6 minus 6, so that gives us 0.
01:37
So this just gives us a determinant of 1.
01:39
Next, we need to find the transpose of m minus 1.
01:48
So we're just going to flip the rows and columns.
01:54
1, 0, 1, 3, and then this 3 stays where it is, that 3 stays where it is, 2 comes up here, and then we have 2, 4...