Given that `a alpha^2 + 2balpha + c != 0` and that the system of equations `(a alpha+b)x+alphay + bz = 0 , (balpha+c)x+by + cz = 0 ,(a alpha+b)y + (balpha + c) z = 0` has a non trivial solution, then a, b,c are in

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0, alphax+(alpha+b)y+alphaz=0, alphax+alphay+(alpha+c)z=0 has a non-trivial solution if

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0, alphax+(alpha+b)y+alphaz=0, alphax+alphay+(alpha+c)z=0 has a non-trivial solution if

The system of equations ax+by+(a alpha+ b)z=0 bx+cy+(b alpha+c)z=0 (a alpha+b)x+(balpha+c)y=0 has a non zero solutions if a,b,c are in

If pqrne0 and the system of equations (p + a) x + by + cz = 0 , ax + (q + b)y + cz = 0 ,ax + by + (r + c) z =0 has a non-trivial solution, then value of (a)/(p) + (b)/(q) + (c )/(r ) is a)-1 b)0 c)1 d)2

Let lambda and alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+ (sin alpha) y + (cos alpha)z = 0 , x + (cos alpha) y + (sin alpha) z = 0 , -x + (sin alpha) y - (cos alpha) z = 0 has a non trivial solution then S contains a) (-1,1) b) [-sqrt2,-1] c) [1,sqrt2] d) [-sqrt2,sqrt2]

If the system of linear equation x + 4ay + ax = 0 , x + 3b + bz = 0 x + 2cy + cz = 0 have a non-trivial solution, then a, b, c are in

The value of alpha for which the system of linear equations: x+(sin alpha)y+(cos alpha)z=0,x+(cos alpha)y+(sin alpha)z=0,-x+(sin alpha)y+(-cos alpha)z=0 has a non - trivial solution could be