00:01
All right, we are asked to solve this system of equation using a matrix.
00:07
What we want to do is the first step is just go in the order x, y answer.
00:14
And so this bottom one, what i want to do is take this 8x and i want to move this back over here.
00:20
So that's going to be negative 8x plus y is equal to negative 12.
00:27
All right.
00:28
Now let's put that into matrix form.
00:30
So this is going to be 4.
00:32
This will be negative 8.
00:34
We have a 3, 1, and then we're going to have a negative 8 and negative 12.
00:42
All right.
00:43
Now, using matrices, one option we could do is we could use what's called kramer's rule.
00:50
All right.
00:50
And here's what we do.
00:51
We're going to take our x and y matrix.
00:53
So 4, negative 8, 3, and 1.
00:56
And what we're going to do is we're going to find what's called the determinant.
01:01
And for the determinant, what we're going to do is we're going to multiply our.
01:04
Our two diagonals.
01:05
So we're going to do four times one.
01:09
And then we're going to subtract the other diagonal, which is a negative eight times three.
01:16
All right.
01:16
So what does that give us? that gives us four.
01:19
That's going to be plus 24.
01:22
And so that's going to be 28.
01:23
So we're going to save this.
01:24
This is going to be useful for us in a second.
01:27
Now what kramer's rule says is that we're going to take these answers.
01:32
And if i want to find the x value, i need to take these answers and i need to put them in for the x spot.
01:39
So i'm going to have negative 8 and negative 12 in this spot instead of the 4 and the negative 8.
01:47
The y's we're going to leave here, 3 and 1.
01:49
And we're going to do that same step again...