Let `lambdaa n dalpha` be real. Find the set of all values of `lambda` for which the system of linear equations `λx+(sinα)y+(cosα)z=0`, `x+(sinα)y−(cosα)z=0`, `−x+(sinα)y+(cosα)z=0` has a non-trivial solution.

The number of integral values of a for which the system of linear equations x sin theta -2 y cos theta -az=0 , x+2y+z=0,-x+y+z=0 may have non-trivial solutions, then

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

The set of all values of lambda for which the system of linear equations x - 2y - 2z = lambdax x + 2y + z = lambday -x -y = lambdaz has a non-trivial solution

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

the value of theta for which the system of equations (sin 3theta)x-2y+3z=0, (cos 2theta)x+8y-7z=0 and 2x+14y-11z=0 has a non - trivial solution, is (here, n in Z )

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 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

Find the value of lambda for which the homogeneous system of equations: 2x+3y-2z=0 , 2x-y+3z=0 , 7x+lambday-z=0 has non-trivial solutions. Find the solution.

Find the real values of lambda for which the following system of linear equations has non-trivial solutions. Also, find the non-trivial solutions. 2lambdax-2y+3z=0 x+lambday+2z=0 2x+lambdaz=0

Find the real values of lambda for which the following system of linear equations has non-trivial solutions. Also, find the non-trivial solutions. 2lambdax-2y+3z=0 x+lambday+2z=0 2x+lambdaz=0