Since the system of linear equations are x+y+z=2 .....(1) 2x+3y+2z=5 .....(2) 2x+3y+(a2−1)z=a+1 .....(1) Now, Δ=|
1
1
1
2
3
2
2
3
a2−1
| (Applying R3→R3−R2) ⇒Δ=|
1
1
1
2
3
2
0
0
a2−3
| =a2−3 When, Δ=0⇒a2−3=0⇒|a|=√3 If a2=3, then plane represented by eqn (2) and eqn (3) are parallel. Hence, the given system of equation is inconsistent.