00:01
In this question, we're given a system of equations, where we have three equations, three unknowns, and we're asked to write this as an augmented matrix and then use row reduction to try to get our solution.
00:13
So when we have an augmented matrix with row reduction, our goal is to get the identity matrix on the left -hand side of the augmented matrix, and then your solutions are all going to be on the right -hand side.
00:29
So i'm going to write the coefficients here first.
00:33
So for that first equation, that's going to be 1, negative 1, negative 1.
00:40
For the second equation, the coefficients are negative 1, 2, negative 3.
00:45
And for this third equation, the coefficients are 3, negative 2, negative 7.
00:52
Now, the augmented part comes from the solutions.
00:56
So the solutions are 1, negative 4, and 0.
01:02
So again, we're trying to get the left -hand side of this to look like the identity matrix.
01:08
And first thing i'm going to try and do is i'm going to multiply my second row here by three, and i'm going to add that to row three.
01:22
And that's going to make my new row three.
01:26
So if i do that, i have not changed anything in the first or second row, so those are going to stay the same.
01:33
1, negative 1, negative 1, 1, 2, negative 3, negative 4.
01:41
But now this third row, if i multiply the second one by 3, and add it to the third row, we're going to get negative 3 plus a positive 3, which will give 0.
01:54
Then we're going to get 6 plus a negative 2, which will give us a 4.
02:00
And we're going to get negative 9 plus a negative 7, which will give us a negative 16.
02:08
And then we're going to get negative 12 plus 0, which will give us a negative 12.
02:20
Okay.
02:23
Now i'm going to try and do a couple things.
02:28
First, i'm going to add row 1 plus row 2.
02:35
I'm going to place those into row 2...