The system of equations `-2x+y+z=a`, `x-2y+z=b`, `x+y-2z=c`, has:
(a)no solution if `a+b+c!=0`
(b)unique solution if `a+b+c=0`
(c)infinite number of solutions if `a+b+c=0`
(d)none of these

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

If x and y are complex numbers, then the system of equations (1+i)x+(1-i)y=1,2i x+2y=1+i has (a) Unique solution (b) No solution (c) Infinite number of solutions (d) None of these

If the system of equation {:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):} have at least one solution, then the relationalship between a,b,c 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

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

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

The number of real solutions of the (log)_(0. 5)(x)=|x| is (a) 1 (b) 2 (c) 0 (d) none of these

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

Given that the system of equations x=cy+bz,y=az+cx,z=bx+ay has non-zero solutions and atleast one of a,b,c is a proper fraction. a^2+b^2+c^2 is

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]|