00:01
Okay, we want to use gauss elimination to solve for x, y, and z.
00:03
We're given our equations, so let's draw our matrix here.
00:09
So we have negative x plus 2y plus 2z equals negative 24.
00:19
X plus y plus z equals 48.
00:24
2x minus 6y plus 4z equals 12.
00:32
Okay, so remember x, y, z.
00:35
Those are the columns.
00:36
Okay, and then we're just applying row operations so we can add rows together.
00:43
We can divide individual rows by constants.
00:47
And we're just trying to get so that the first part of the matrix is like 0, 0, 1, 1, 0, 0, 0, 1, 0, and then there's like constants here, right? we're just trying to get it so that we get like two 0s and a 1, and a 1 and two 0s, and a 0 and a 1 and a 0, something like that.
01:12
Which when you convert it back to the equation form, it would be like z equals the constant, and x equals a constant, y equals a constant, right? so a quick review of gauss elimination.
01:32
So first operation, let's take row 1 plus row 2.
01:43
Okay, so we're going to get 0, 3, 3, 24, 1, 1, 1, 48, 2 minus 6, 4, 12.
01:57
So we just added the second row to the first row.
02:01
And then let's simplify this.
02:03
So divide the first row by 3, divide the second row, or the third row by 2.
02:17
And i'll try to make the matrices a little bit bigger so we don't get confused about rows here.
02:23
Okay, next let's take row 2, or let's see, negative row 2, and add it to row 3.
02:37
So the first row is unchanged, 0, 1, 1, 8.
02:40
Second row is unchanged, 1, 1, 1, 48...