Test the consistency and solve them when consistent the following system of equations for all values of `lambda:` `x+y+z=1` `x+3y-2z=lambda` `3+(lambda+2)y-3z=2lambda+1`

Determine the values of lambda for which the following system of equations fail to have a unique solution: lambda x+3y-z=1,x+2y+z=2,-lambda x+y+2z=-1

Find the real values of lambda for which the following system of linear equations has non -trivial solutions: x+y-3z=0,( 1+lambda)x+(2+lambda)y-8z=0 , x-(1+lambda)y+(2+lambda)z=0 .

The value of lambda , such that the following system of equations has no solution, is x - 2y + z = - 4 2x - y - 2z = 2 x + y + lambda z = 4

Determine the values of lambda for which the following system of equations: lambda x+3y-z=1x+2y+z=2-lambda x+y+2z=-1 has non-trival solutions.

Find the real values of lambda for which the following system of linear equations has non- trivial solutions.Also,find the non-trivial solutions.2 lambda x-2y+3z=0x+lambda y+2z=02x+lambda z=0

For which value of lambda , plane 4x + 6y -2z =8 and 2x+3y+ lambda z= 12 are parallel?

Determine the values of lambda for which the following system of equations : lambdax+3y-z=1 , x+2y+z=2 , -lambdax+y+2z=-1 has non-trival solutions.

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

The system of linear equations lambda x + y + z = 3 x - y - 2z = 6 -x + y + z = mu has

For which value of "lambda" ,planes "4x+6y-2z=8" and "2x+3y+lambda z=12" are parallel?