for the following linear system, put the augmented coefficient matrix into reduced row-echelon form.
2x1 + 3x2 − x3 = 14
x1 + 2x2 + x3 = 4
5x1 + 9x2 + 2x3 = 7

The augmented matrix of the system is .

We apply operations rows:

1. We swap row 1 and 2 and obtain the matrix .

2. Of the above matrix we subtract row 1 from row 2 twice (R2 - 2R1) and we subtract row 1 from row 3, 5 times. (R3-5R1). We obtain the matrix

3. Of the above matrix we subtract row 2 from row1 twice (R3 - R2) and multiply the row 1 by -1 (-R2). Weobtain the matrix .

Since each pivote is an one then we conclude that the above matrix is the reduced row-echelon form of the matrix of the system.

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: