Statement 1: If the system of equation `lambdax+(b-a)y+(c-a)z=0,(a-b)x+lambday+(c-b)z=0,a n d(a-c)x+(b-c)y+lambdaz=0` has a non trivial solution, then the value of `lambda` is 0. Statement 2: the value of skew symmetric matrix of order 3 is Zero.

The system of homogeneous equation lambdax+(lambda+1)y +(lambda-1)z=0, (lambda+1)x+lambday+(lambda+2)z=0, (lambda-1)x+(lambda+2)y + lambdaz=0 has non-trivial solution for :

if the system of equations (a-t)x+by +cz=0 bx+(c-t) y+az=0 cx+ay+(b-t)z=0 has non-trivial solutions then product of all possible values of t is

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 .

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 a. -1 b. 0 c. 1 d. 2

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 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 a/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

If the system of equations {:(x-lamday-z=0),(lamdax-y-z=0),(x+y-z=0):}} has unique solution then the range of lamda is R-{a,b} Then the value of (a^(2)+b^(2)) is :

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

Prove that the system of equations in xa +y+z=0 , x +by +z=0 , x +y+cz=0 has a non - trivial solution then 1/(1-a) + 1/(1-b)+ 1/(1-c)=

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 .