00:01
In this question, we are asked to find the solution of the given system of equations.
00:05
And to do that, we first need to write down its augmented matrix, which is basically a matrix consisting of the coefficients in front of x, y, and z, and the right -hand sides.
00:27
So, this is an augmented matrix of our system of equations.
00:31
Now we need to reduce it to a row echelon form.
00:34
And we will start by getting rid of the numbers below the first one.
00:42
And to do that, we need to multiply the first row by negative 3 and add it to the second row, and multiply the first row by negative 2 and add it to the third row.
00:53
We will rewrite the first row.
01:04
And in the second row, we will get 1 times negative 3 is negative 3, plus 3 is 0.
01:14
2 times negative 3 is negative 6.
01:16
Negative 6 plus 7 equals to 1.
01:20
3 times negative 3 is negative 9.
01:22
Negative 9 plus 8 equals to negative 1.
01:25
And finally, 30 times negative 3 is negative 90.
01:32
Negative 90 plus 87 is negative 3.
01:36
Now let's move on to the third row.
01:39
1 times negative 2 plus 2 is going to be 0.
01:46
2 times negative 2 is negative 4.
01:49
Negative 4 plus 5 equals to 1.
01:53
3 times negative 2 is negative 6.
01:56
And negative 6 plus 7 equals to 1.
02:01
And 30 times negative 2 is negative 60.
02:04
And negative 60 plus 71 equals to 11...