how do you solve this system using the row reduction method?

Question

x - 2y - z = 3
x + y +2z = 9
2x + 3y + z = 0

show work please. :) THANKS!!!

Answer 1

Your given matrix is

[1 -2 -1 3]
[1 1 2 9]
[2 3 1 0]. Add appropriate multiples of row 1 to rows 2 and 3 to get

[1 -2 -2 3]
[0 3 3 6]
[0 7 3 -6]. Multiply row 2 by 1/3, then add appropriate multiples to the other rows to get

[1 0 1 7]
[0 1 1 2]
[0 0 -4 -20]. Multip[ly row 3 by -1/4, then add multiples to rows 1 and 2 to get

[1 0 0 2]
[0 1 0 -3]
[0 0 1 5].

Thus, your solution is x = 2, y = -3, and z = 5.