The system of equations `2x - y + z = 0,x-2y + z = 0 and lambdax - y + 2z = 0` has infinite number of non-trivial solution for

The system of equations 2x-y+z=0,x-2y+z=0 and lambda x-y+2z=0 has infinite number of non-trivial solution for

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution

The system of equations lambda x + y + 3z = 0, 2x + mu y - z = 0, 5x + 7y + z = 0 has infinitely many solutions in R. Then,

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

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

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

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