00:01
Alright, so here we are given a matrix a, 100, x ,10, zy1, and we are told that a squared plus 0 -00 -0 -0 -negative -1 -0 is equal to the 3x3 identity matrix.
00:19
So we need to figure out what x, y, and z are.
00:23
So the way that we can do that is first, let's figure out what a squared is.
00:28
So a squared is going to be a times a, which is going to be, i'm just going to copy these guys down.
00:40
That paste, yes, there we go.
00:45
So only real way to figure out what the square of a matrix is, unless it's in a very particular form, is to do the matrix multiplication by hand.
00:54
So the ijth element of our product here is going to be the dot product of row i, from this guy on the left with column j, and this guy on the right.
01:05
So, element 1 -1 is going to be 1 times 1 plus x times 0 plus x times 0, that's just going to be 1.
01:13
Element 1 -2, sorry, actually i'm going to go to 1.
01:17
0 times 1 plus 1 times 0 plus y times 0 is 0.
01:21
3 1, 0 times 1 plus 0 plus 1 times 0 is 0.
01:26
1 2 is going to be 1 times x plus x times 1 plus x times 0, so that's going to be 2x up there.
01:36
Element 2 2, 0 times x plus 1 plus y times 0, it's going to be positive 1.
01:45
Element 3, 2, is going to be 0 times x plus 0 times 1 plus 1 times 0.
01:51
It's going to be 0.
01:54
Element 1 3 is going to be 1 times z plus x times y plus z times 1.
02:03
So we get two, sorry, yes, that would be 2z plus xy is our element 13 there.
02:17
Element 2 .3 is going to be 0 times z plus 1 times y, plus y times 1...