The greatest value of `c in R` for which the system of linear equations x-cy-cz = 0, cx -y + cz =0, cx + cy-z =0 has a non-trivial solution, is

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambdaz=0 has a non-trivial solution for

The value of a for which the system of linear equations ax+y+z=0, ay+z=0,x+y+z = 0 possesses non-trivial solution is

The value of a for which the system of linear equations ax+y+z=0,ay+z=0,x+y+z=0 possesses non-trivial solution is

If the system of linear equation x + 4ay + ax = 0 , x + 3b + bz = 0 x + 2cy + cz = 0 have a non-trivial solution, then a, b, c are in

If the system of linear equations x + 2ay + az = 0 , x + 3by + bz = 0 , x + 4cy + cz = 0 has a non-zero solution, then a, b, c

The system of equations ax + 4y + z = 0,bx + 3y + z = 0, cx + 2y + z = 0 has non-trivial solution if a, b, c are in