The system of linear equations kx + y + z =1, x + ky + z =1 and x+y+k z=1 has a unique solution under which one of the following conditions?

Step-by-step solution

Linear equations aligned & K x+y+z=1 & x+K y+z=1 & x+y+K z=1 & [ array ccc K & 1 & 1 1 & K & 1 1 & 1 & K array ] [ array l x y z array ]= [ array l 1 1 1 array ] & A X=B & X=A⁻¹ B aligned Linear equation will have unique solution when A⁻¹ exist : aligned & |A| 0 & [ array ccc K & 1 & 1 1 & K & 1 1 & 1 & K array ] 0 & K (K^2-1 )-1(K-1)+1(1-K) 0 & K^3-K-K+1+1-K 0 & K^3-3 K+2 0 aligned aligned & (K-1) (K^2+K-2 ) 0 & (K-1)(K-1)(K+2) 0 & K 1, K 1 and K -2 & K 1 and K -2 aligned