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 + 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 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

If the system of equations x= cy +bz, y=az +cx and z=bx+ay has a non - trivial solution then

If p q r!=0 and the system of equation (p+a)x+b y+c z=0 a x+(q+b)y+c z=0 a x+b y+(r+c)z=0 has nontrivial solution, then value of a/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

If p q r!=0 and the system of equation (p+a)x+b y-c z=0 a x+(q+b)y+c z=0 a c+b y+(r+c)z=0 has nontrivial solution, then value of 1/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

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