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

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

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

The system of equations 6x+5y+ lamda z= 0, 3z-y+4z= 0, x+2y-3z=0 has non-trivial solutions for

If the system of equation : x + y + z = 0 , 2 x + 3y + 4z = 0 , kx + y - z = 0 has a non - zero solution , then the value of k is

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 system of linear equations x + lambda y-z =0, lambdax-y -z =0, x + y -lambda z =0 has a non-trivial solution for

The system of equations: x+ky+3z=0 , 3x+ky-2z=0 , 2x+3y-4z=0 has non- trivial solution. when k=