The system of equations `lambdax + (lambda+ 1) y+ (lambda- 1)z=0,(lambda+1)x+lambday+(lambda+z)z=0,(lambda-1)x+(lambda+2)y+lambdaz=`bas a non-trivial solutions for

The system of equations lambda x+(lambda+1)y+(lambda-1)z=0,(lambda+1)x+lambda y+(lambda+z)z=0,(lambda-1)x+(lambda+2)y+lambda z= bas a non-trivial solutions for

The system of homogeneous equation lambdax+(lambda+1)y +(lambda-1)z=0, (lambda+1)x+lambday+(lambda+2)z=0, (lambda-1)x+(lambda+2)y + lambdaz=0 has non-trivial solution for :

The equation (lambda-1)x+(3lambda+1)y+2lambdaz=0 . (lambda-1)x+(4lambda-2)y+(lambda+3)z=0 and 2x+(3lambda+1)y+3(lambda-1)z=0 gives non-trivial solution for some values of lambda, then the ratio x : y : z when lambda has the smallest of these values :

The sum of distinct value of lambda for which the system of equations (lambda -1 )x + (3lambda + 1) y + 2 lambda x= 0 (lambda -1) x + (4lambda - 2) y + (lambda + 3) x= 0 2x + (2lambda + 1) y + 3(lambda - 1) z=0 has non - zeor solutions is ______.

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0, (lambda-1)x+(4lambda-2)y+(lambda+3)z=0, 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

Find all values of lambda for which the (lambda-1)x+(3 lambda+1)y+2 lambda z=0(lambda-1)x+(4 lambda-2)y+(lambda+3)z=02x+(3 lambda+1)y+3(lambda-1)z possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

The system of linear equations x + lambda y-z =0, lambdax-y -z =0, x + y -lambda z =0 has a non-trivial solution for

A system of equations lambdax +y +z =1,x+lambday+z=lambda, x + y + lambdaz = lambda^2 have no solution then value of lambda is