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. 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

If 0lt= thetalt=pi and the system of equations x+(sin theta)y- (costheta) z =0, (cos theta ) x-y+z=0, (sin theta) x+y-z=0 has a non -trivial solution then theta is

Find |A| if A=[{:(0,sinalpha,cosalpha),(sinalpha,0,sinbeta),(cosalpha,-sinbeta,0):}]

For what value of lambda , the system of equations x+y+z=1, x+2y+4z= lambda , x+4y+10z= lambda^(2) is consistent

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.

the set of equations lambdax-y+(cos theta) z=0,3x+y+2z=0 , (cos theta) x+y+2z=0 , theta le 0 lt 2 pi has non-trivial solution (s)

The system of linear equations x+y+z =2, 2x+y-z=3, 3x+2y+kz= has a unique solution if