If the system of linear equations `x + 2ay + az = 0`,`x + 3by + bz = 0`,`x + 4cy + cz = 0` has a non-zero solution, then `a, b, c`

If the system of linear equation x + 2ay + az = 0, x + 3by + bz = 0, x + 4cy + cz = 0 has a non-trival solution then show that a, b, c are in H.P.

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

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are -1,2 b. 1,2 c. 0,1 d. -1,1

The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=c where a,b and c are non-zero real numbers, has more than one solution, then

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 .

The system of linear equations x+y+z =2, 2x+y-z=3, 3x+2y+kz= has a unique solution if