IIT JEE 2008 question II

for these equations determinant =0

now the system of equations has infinite solutions or no solutions depending on \Deltax,\Deltay,\Deltaz is non-zero , then it has no solution otherwise infinite solutions

but \Deltax=0 if k=3

\Deltay=0 if k=3
\Deltaz=0 if k=3

thus the system of equations has no solutions for k≠3.

hence answer is A

Using Cramer's rule

D=0
(A)
1 -2 3
D -1 1 -2 = 0
1 -3 4

and
-1 -2 3
D1 k 1 -2 = (3- k)= 0
1 -3 4
if k = 3-------------(1)

1 -1 3
D2 -1 k -2 = (k - 3) =0
1 1 4
if k=3
1 2 1
D3 1 1 k = (k -3) = 0
1 3 1
if k = 3

⇒ system of equations has no solution for k ≠3.

Therefore A..

[56]

ans is b