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 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

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

Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=0x+(cosalpha)y+(sinalpha)z=0x-(sinalpha)y-(cos\ alpha)z=0 has a non-trivial solution for only value of alpha lying the interval (0,\ pi/2) Statement 2: The equation in\ alpha |cosalphas in\ alphacosalphasinalphacosalphasinalphacosalpha-sinalpha-cosalpha|=0 has only one solution lying in the interval (0,\ pi/2) Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

The set of all values of lambda for which the systme of linear equations x-2y-2z = lambda x, x +2y +z = lambda y " and "-x-y = lambdaz has a non-trivial solution.