Answer
Replace row 2 with the sum of it and 3 times row 3,
then replace row 1 with the the sum of it and -5 times row 3.
Work Step by Step
When we want to solve a system of linear equations in an augmented matrix, we want to first put it in a triangular form(which is a term to be replaced in the next section).
Then we want to use the leading(from the left) 1 in each row to eliminate the entries within the same column.
The matrix given to us is
1 -4 5 0 7
0 1 -3 0 6
0 0 1 0 2
0 0 0 1 -5
Since it is already in triangular form, and has already cleared out all but 1 entry on the first row from the right, we must clear out all but 1 entry from the 2nd row from the right.
In order for us to do so, we must add 3 times the 3rd row to the 2nd row, and subtract 5 times the 3rd row from the 1st row. These two operations give us a new matrix:
1 -4 0 0 -3
0 1 0 0 12
0 0 1 0 2
0 0 0 1 -5
Which is closer to the solved stated of an augmented matrix.
