00:01
In this question we are asked to solve the given system of linear equations and the first step is to construct the augmented matrix which is basically a matrix consisting of the containing the coefficients in front of x1 x2 and x3 and the right -hand sides the first row is going to be 1 2 2 12 right which corresponds to the first equation the second row is going to be 8 4 4 24 and the last row is going to be 3, 3, 9 and 18.
00:39
Now we need to reduce this matrix to a row echelon form, and to do that, we will multiply the first row by negative 8 and add it to the second row, and we will multiply the first row by negative 3 and add it to the last row.
01:03
Let's rewrite the first row because we are not changing the first row, in the second row, we are going to get 1 times negative 8 plus 8 is going to be 0.
01:18
2 times negative 8 is negative 16, and negative 16 plus 4 equals to negative 12.
01:26
2 times negative 8 is negative 16, negative 4 is negative 12.
01:33
12 times negative 8 is negative 96.
01:37
Negative 96 plus 24 is going to be negative 72.
01:45
Let's move on to the third row.
01:48
1 times negative 3 plus 3 is going to be 0.
01:51
2 times negative 3 is negative 6 plus 3 is going to be negative 3 2 times negative 3 is negative 6 plus 9 is going to be 3 and 12 times negative 3 is negative 36 negative 36 plus 18 equals to negative 18 what we're going to do next is we will divide the second row by 12 by negative 12 we will write the first row in the second row, we are going to get 0, 1, 1, and negative 72 over negative 12 equals to 6.
02:52
And we will divide the third row by negative 3...