Verified answer

3x -2y +z=-5

-2x +3y -3z =12

3x -2y -2z =4

[ 3 -2 1 | -5 ]

[-2 3 -3 | 12]

[ 3 -2 -2| 4 ]

L₃→L₃-L₁

L₂→L₂+(2/3)L₁

[ 3 -2 1 | -5 ]

[0 5/3 -7/3|26/3 ]

[0 0 -3 | 9 ]

L₂→(3/5)L₂

[ 3 -2 1 | -5 ]

[ 0 1 -7/5| 26/5 ]

[ 0 0 -3 | 9]

L₁→L₁+2L₂

L₃→(-1)L₃

[ 3 0 -9/5 | 27/5 ]

[ 0 1 -7/5 | 26/5]

[ 0 0 3 | -9 ]

L₃→(1/3)L₃

[ 3 0 -9/5 | 27/5 ]

[ 0 1 -7/5 | 26/5]

[ 0 0 1 | -3 ]

L₂→L₂+(7/5)L₃

L₁→(1/3)L₁

[ 1 0 -3/5 | 9/5 ]

[ 0 1 0 | 1 ]

[ 0 0 1 | -3 ]

L₁→L₁+(3/5)L₃

[ 1 0 0 | 0 ]

[ 0 1 0 | 1 ]

[ 0 0 1 | -3]

1x =0

1y=1

1z =-3

x=0 , y=1 , z=-3

option 3 is correct