Let `lambdaa n dalpha` be real. Find the set of all values of `lambda` for which the system of linear equations `lambdax+(sinalpha)y+(cosalpha)z=0,x+(cosalpha)y+(sinalpha)z=0,-x+(sinalpha)y-(cosalpha)z=0.` have trivial solution

Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains

The value of alpha for which the system of linear equations: x+(sin alpha)y+(cos alpha)z=0,x+(cos alpha)y+(sin alpha)z=0,-x+(sin alpha)y+(-cos alpha)z=0 has a non - trivial solution could be

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

Let lambda and alpha be real. Find the set of all values of lambda for which the system of linear equations lambdax + ("sin"alpha)y + ("cos" alpha)z =0 , x + ("cos"alpha)y + ("sin" alpha) z =0 and -x + ("sin" alpha)y -("cos" alpha)z =0 has a non-trivial solution. For lambda =1 , find all values of alpha .

Let lamda and alpha real. Find the set of all values of lamda for which the system. x+(sinalpha)y+(cosalpha)z=0, x+(cosalpha)y+(sinalpha)z=0, -x+(sinalpha)y+(cosalpha)z=0 has a non trivial solution. For lamda=1 find all values of alpa.

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

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 values of theta , lambda for which the following equations sinthetax-costhetay+(lambda+1)z=0 , costhetax+sinthetay-lambdaz=0 , lambdax+(lambda+1)y+costhetaz=0 have 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