00:01
Let's say we're given this system of equations and we want to solve this by using a matrix, right? because solving a matrix, sorry, solving a system with three unknowns can take a lot of steps if we're trying to do it manually.
00:16
So the first thing that we want to do is we want to create what's called a coefficient matrix.
00:20
That means we're going to take all the coefficients here and i'll just underline them, right? and anytime there's a number not in front of something, then you can say that that coefficient is 1.
00:32
So these are really 1 -1 -negative 1 here.
00:36
So we have 1 -1 -negative 1.
00:39
We have 2 -7 -4, and then we have 2 -9 -7.
00:45
So this is our coefficient matrix.
00:47
We're going to multiply it by our variable matrix, that's just x, y, z, because that's the order that we have them in on the left side.
00:55
And then this is going to be equal to your solutions matrix, which is basically all of these numbers here, 8, negative 1, and 9.
01:03
All right.
01:04
So 8, negative 11, and 9.
01:10
Okay.
01:12
Great.
01:14
So now the way that, like, we can solve this is we got to move this big matrix to the other side...