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 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.Find the set of all values of lambda for which the system of linear equations lambda x+(sin alpha)y+(cos alpha)z=0,x+(cos alpha)y+(sin alpha)z=0,quad -x+(sin alpha)y-(cos alpha)z=0

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.

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.

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

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

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 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. 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