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

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:

x+ky-z=0 , 3x-ky-z=0 and x-3y+z=0 has non-zero solution for k=

If the system of equations x+a y=0,a z+y=0 and a x+z=0 has infinite solutions, then the value of a is (a) -1 (b) 1 (c) 0 (d) no real values

If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite solutions, then the value of equation has no solution is -3 b. 1 c. 0 d. 3

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 :

If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+c z=0 has a non zero solution then (a) System is always non trivial solutions (b) System is consistent only when a=b=c (c) If a!=b!=c then x=0,\ y=t ,\ z=-t\ AAt in R (d) If a=b=c\ t h e n\ y=t_1, z=t_2,\ x=-a(t_1+t_2)AAt_1, t_2 in R

If the system of equations, x+2y-3z=1,(k+3)z=3,(2k+1)x+z=0 is inconsistent, then the value of k is (A) -3 (B) 1/2 (C) 0 (D) 2

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 _________.

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 equations kx+(k+2)y+(k-2)z=0, (k+2)x+ky+(k+4)z=0 (k-2)x+(k+4)y+kz=0 has a non - trivial solution for