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 a is, a.`-3` b. `-1` c. `0` d. `3`

If a inRR and the system of equations x+ay=0, az+y=0 , ax+z=0 has infinite number of solution then the value of a is

If the system of equations x+y+z=6, x+2y+kz=0 and x+2y+3z=10 has no solution, then the value of k is -

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 lambdax+y+3z=0,2x+muy-z=0,5x+7y+z=0 has infinitely many solutions in R. Then

If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solution, find the value of adot

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

If the system of equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + alphaz = beta has infinitely many solution, then beta - alpha equals

Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-5y+4z=lambda is consistent and find the solutions for all such values of lambdadot

The values of k in R for which the system of equations x+k y+3z=0,k x+2y+2z=0,2x+3y+4z=0 admits of nontrivial solution is a. 2 b. 5//2 c. 3 d. 5//4

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|