The value of ' a ' for which the system of equations a x+y+z=0, x+a y+z=0, x+y+z=0 possesses non-zero solutions are given by

Step-by-step solution

Given, system of equations are aligned & a x+y+z=0, x+a y+z=0 & and x+y+z=0 possesses non-zero solution. aligned | array lll a & 1 & 1 1 & a & 1 1 & 1 & 1 array |=0 array rr & a(a-1)-1(1-1)+1(1-a)=0 & a^2-a+0+1-a=0 & a^2-2 a+1=0 & (a-1)^2=0 & a=1 array