For what value of k, does the following system of equations possess a non-trivial solution over the set of rationals x+y-2z=0, 2x-3y+z=0 and x-5y+4z=k. Find all the solutions.

For what values of k, the following system of equations possesses a nontrival solution over the set of rationals: c+ky+3z=0,3c+ky-2z=02c+3y-4x=0 Also find the solution for this value of k.

For what value of K do the following system of equations possess a non trivial (i.e. not all zero) solution over the set of rationals Q ? x + K y + 3 z = 0 , 3 x + K y - 2 z = 0 , 2 x + 3 y - 4 z = 0 . For that value of K , find all the solutions of the system.

For what value of k the following system of linear equations wil have infinite solutions x-y+z=3, 2x+y-z=2 and -3x-2ky+6z=3

The equations x+y-2z=0,2x-3y-z=0,x-5y+4z=k have non-zero solutions if k=

If the system of equations x+y+2z=0,2x-3y+z=0,x-5y+4z=lambda has a non trival solution then

If the system of equations x+y+z=0 ax+by+z=0 bx+y+z=0 has a non trivial solution then

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 values of k for which the system of equations kx+y+z=0,x-ky+z=0 and x+y+z=0 possesses non-trivial solution. Are

The number of non-trivial solutions of the system x=y+z=0, x+2y-z=0, 2x+y+3z=0 , is