`x - 3z = -2, 3x + y - 2z = 5, 2x + 2y + z = 4` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

`x-3z=-2`

`3x+y-2z=5`

`2x+2y+z=4`

The equations can be written as

`[[1,0,-3,|-2],[3,1,-2,|5],[2,2,1,|4]]`

R2 `->` (R1+R3)-R2

`[[1,0,-3,|-2],[0,1,0,|-3],[2,2,1,|4]]`

R3 `->` (R3-2R2)

`[[1,0,-3,|-2],[0,1,0,|-3],[2,0,1,|10]]`

R1`->` (2R1-R3)

`[[0,0,-7,|-14],[0,1,0,|-3],[2,0,1,|10]]`

R3 `->` (7R3+R1)

`[[0,0,-7,|-14],[0,1,0,|-3],[14,0,0,|56]]`

`-7z=-14`

`z=(-14)/(-7)=2`

`y=-3`

`14x=56`

`x=56/14=4`

Solutions of the equation are x=4,y=-3,z=2