For in consistent system of equations [Δ=0 and atleast one is non-zero in Δ1,Δ2 and .Δ3] Δ=|
−1
1
2
3
−a
5
2
−2
−a
|=0 ⇒ a2−7a+12=0 ⇒ a = 3, 4 Δx=|
0
1
2
1
−a
5
7
−2
−a
|=15a+31 Δx≠0 for a=3,4 ⇒ n(S1)=2 Now, for infinitely many solutions. If Δ=0 also Δx=Δy=Δz=0 Which is not possible for any real value of a ⇒ n( S2) = 0