00:01
Section 3 .2, problem 29, they give us a 2x2 matrix a, 2x2 matrix b.
00:06
They tell us the determinant of a is 1 and find the determinant of b.
00:11
So the key here is to find what is the transformation that happened to get me from a to b? so if i started out with matrix a, so a is a, b, c, d.
00:25
If you look at in matrix b, it looks like there's a c here instead of a b, and there's a b here instead of a c.
00:33
So that looks like there's a transpose that happened.
00:36
So if you were to transpose that matrix, that would get you a, c, b, d.
00:47
Then what is the transformation that would take you further? what would happen if i did negative 2 times row 1, then that transformation, would end up with what negative 2a, negative 2c? and what if i were to take, the other transformation would be 3 times row 1 plus row 2, that would give me 3a plus b, and then 3c plus d.
01:21
So that's the transformation that gets me from a to b.
01:26
So we've got to see, what did these transformations, what effect did they have on the determinant? okay.
01:32
Well, the transpose has no effect because the determinant of a is equal to the determinant of a transpose.
01:42
Okay.
01:43
So that made no change for me...