Solve by using matrices. 2x – y +2 + w = -3 x + 2y – 3z + w = 12 3x - y - + 2w = 3 -2x + 3y + 2 – 3w = -3​

Some symbols and numbers are missing. I assume the system is supposed to read

2x - y + 2z + w = -3

x + 2y - 3z + w = 12

3x - y - z + 2w = 3

-2x + 3y + 2z - 3w = -3

In matrix form, this is

which we can strip down to the augmented matrix,

Now for the row operations:

• swap rows 1 and 2

• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4

• add 7 (row 2) to -5 (row 3), and row 3 to row 4

• multiply through rows 3 and 4 by 1/2

• add -4 (row 4) to row 3

• swap rows 3 and 4

• multiply through row 4 by 1/3

• add row 4 to row 3

• multiply through row 3 by 1/2

• add -8 (row 3) and row 4 to row 2

• multiply through row 2 by -1/5

• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1

Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).