If the system of equation `x+lambday+1=0,\ lambdax+y+1=0\ &\ x+y+lambda=0.\ ` is consistent the find the value 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

Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-5y+4z=lambda is consistent and find the solutions for all such values of lambdadot

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 c<1 and the system of equations x+y-1=0,2x-y-c=0,and -bx+3b y-c=0 is consistent, then the possible real values of b are

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 .

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 a circle passes through the point of intersection of the lines x+ y +1=0 and x+ lambda y-3=0 with the coordinate axis, then find the value of lambda .

If the equation 3x^2 + 3y^2 + 6lambdax + 2lambda = 0 represents a circle, then the value of lambda . lies in

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 .

For the pair of equations lambdax + 3y + 7 = 0 and 2x + 6y - 14 = 0 . To have infinitely many solutions, the value of lambda should be 1 . Is the statement true ? Give reasons.