The value of a for which system of equation , `a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0, x+y+z=0,` has a non-zero solution is:

The value of a for which system of equation,a^(3)x+(a+1)^(3)y+(a+2)^(3)z=0,ax+(a+1)y+(a+2)z=0,x+y+z=0 has a non-zero solution is:

The value of a for which the system of equations , a^(3)x + (a + 1)^(3) y + (a + 2)^(3) z = 0 , ax + (a + 1) y + (a + 2) z = 0 & x+y+z=0 has a non - zero solution is :

If the system of equations x – ky – z = 0, kx – y – z=0, x + y – z = 0 has a non -zero solution then the possible values of k are

The system of equations ax + y + z = 0 , -x + ay + z = 0 and - x - y + az = 0 has a non-zero solution if the real value of 'a' is