The system of homogeneous equations ,(a-1) x+(a+2) y+a z=0,(a+1) x+a y+(a+2) z=0,a x+(a+1) y+(a-1) z=0has a non-trivial solution if a equals

The system of equations will have a non-trivial solution if ∆ = 0 whereΔ=a-1a+2aa+1aa+2aa+1a-1Using C1→C1-C3 and C2→C2-C3 , we obtain Δ=-12a-1-2a+212a-1Using R3→R3+R2 we get Δ=-12a-1-2a+2002a+1=(2a+1)(2+2)=4(2a+1)Now, Δ=0⇒a=-1/2