If S is the set of distinct values of 'b' for which the following system of linear equations
`x+y+z=1`
`x+ay +z=1`
`ax+by+z=0`
has no solution then S is

If S is the set of distinct values of ' b for which the following system of linear equations x+y+z=1 x+a y+z=1 a x+b y+z=0 has no solution, then S is : a finite set containing two or more elements (2) a singleton an empty set (4) an infinite set

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.

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

If the system of linear equations x+ky+3z=0 3x+ky-2z=0 2x+4y-3z=0 has a non-zero solution (x,y,z) then (xz)/(y^2) is equal to

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

Solve the following system of linear equations by Cramers rule: x+y=5,\ \ y+z=3,\ \ x+z=4

The value of a for which the system of linear equations ax+y+z=0, ay+z=0,x+y+z = 0 possesses non-trivial solution is

Solve the following system of linear equations using matrix method : 3x + y + z = 1, 2x + 2z =0, 5x + y + 2z = 0 .

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

The system of equations ax-y- z=a-1 ,x-ay-z=a-1,x-y-az=a-1 has no solution if a is: