Q1 (10 points)
[i] Solve the following system of linear equations using elementary row operations. If the solution does not exist, state and explain why the solution does not exist.
x−2y+z=−6
−2x+y−2z=6
x+3y−3z=16
[ii] Solve the following system of linear equations using elementary row operations. If the solution does not exist, state and explain why the solution does not exist.
x+y+3z=7
x+2y+4z=11
3x+4y+10z=25
[iii] Solve the following system of linear equations using elementary row operations. If the solution does not exist, state and explain why the solution does not exist.
x+y−z=4
3x−2y+z=−1
2x−3y+2z=0