00:01
In this question, we are asked to solve the given system of linear equations.
00:07
To do that, we first need to create the augmented matrix of the system.
00:12
The augmented matrix consists of the coefficient of the system and the right -hand side.
00:31
Note that even though we don't have the z variable in the first two equations, we are just replacing z by zero.
00:39
Every column in the augmented matrix corresponds to one variable, and the last column corresponds to the right hand side.
00:52
If the variable is absent in the equation, we'll just replace its value in the corresponding column by 0.
01:10
To emphasize that the last column is the right hand side, we put the vertical bar.
01:18
Now we are going to multiply the first row by negative 5 and add it to the second row into the third row.
01:38
We will rewrite the first row.
01:43
And in the second row, we will get 0, 0, 0.
01:50
Negative 5 times 3 plus 15 is 0.
01:55
And negative 5 times 0 plus negative 1 is negative 1.
01:58
Negative 5 times 4 plus 21 is 1.
02:03
In the third row, we will get 0, 0, 1.
02:09
Negative 5 times 3 plus 14 is negative 1.
02:13
Negative 5 times 0 plus negative 2 is negative 2.
02:17
Negative 5 times 4 plus 18 is negative 20 plus 18 is negative 2.
02:31
Now let's exchange the second row and the third rows.
02:41
We will rewrite the first row.
02:46
In the second row, we will get 0 -0 -1, negative 1, negative 2, negative 2.
02:52
And in the last row we will get 0 -0...