3.If the system of equations `x+6y+6z=lambda x`,`4x-y+4z=lambda y`,`2 lambda x+2 lambda y+lambda z=5z` has non-trivial solution then the value of `| lambda|` equals (where `lambda in R` )

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

If the system of linear equations x+ y +z = 5 x+2y +2z = 6 x + 3y + lambdaz = mu, (lambda, mu in R) has infinitely many solutions, then the value of lambda + mu is

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

If the system of equations 3x-2y+z=0, lambda x-14y+15z=0, x+2y+3z=0 have a non trivial solution, then the value of lambda^(2) must be

The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

Let lambda be a real number for which the system of linear equations x + y +z =6, 4x + lambday -lambdaz = lambda -2 and 3x + 2y-4z =-5 has infinitely many solutions. Then lambda is a root of the quadratic equation

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 :

If system of equation x + y + z = 6 ,x + 2y + 3z = 10, 3x + 2y + lambda z = mu has more than two solutions. Find (mu -lambda^2 )

The value(s) of lambda for which the system of equations (1-lambda)x+3y-4z=0 x-(3+lambda)y + 5z=0 3x+y-lambdaz=0 possesses non-trivial solutions .

Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x + 5y + lambdaz=-3 has at least one solution for any real number lambda. Find the set of solutions of lambda =-5