00:01
Alright, so for part a with this whole encrypted cartography idea, they've given us the key and they want us to find the inverse.
00:10
So to do that, we're going to take our matrix and set it up next to an identity matrix.
00:18
And then we're going to flip it so our identity matrix is on the left.
00:24
So i'm going to use this one in my third row to get rid of the numbers above it.
00:30
So row 1 minus 2 row 3 and row 2 minus row 3.
00:39
So 2 minus 2 is 0.
00:42
1 minus 2 is negative 1.
00:45
1 minus 2 is negative 1.
00:47
1 minus 1 is 0.
00:49
1 minus 1 is 0.
00:51
0 minus 1 is negative 1.
00:54
And that row is not changing.
00:58
And then i went 1 minus 0 is 0.
01:02
0 minus 0 is 0.
01:05
0 minus 2 is negative 2.
01:08
0 minus 0.
01:10
1 minus 0 is 1.
01:12
0 minus 1 is negative 1.
01:15
And this one didn't change.
01:18
All right.
01:18
I'm going to use this negative 1 to get rid of the ones above and below it.
01:23
So we're 1 minus row 2 and row 3 plus row 2.
01:31
So that gives me 0 minus 0 0, negative 1 minus 0 is 0, negative 1 minus 0 is 0.
01:37
Negative 1, negative 1 minus negative 1 is 0.
01:41
This row is not changing.
01:44
1 minus 0 is 1, or 1 plus 0 is 1 plus 0 is 0.
01:54
And then for this 1 minus 0 is 1, 0 minus 1 is negative 1.
02:00
Negative 2 minus and negative 1.
02:04
Row 2 did not change.
02:07
And row 3 i added it, so 0 plus 0 is 0.
02:11
0 plus 1 is 1, negative 1 plus 1, or 1 plus negative 1 is 0.
02:18
Alright, last step, we're going to use row 1 to get rid of that 1 in row 3.
02:24
So row 3 plus row 1...