If

$$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{ 0 & {\cos x} & { - \sin x} \cr {\sin x} & 0 & {\cos x} \cr {\cos x} & {\sin x} & 0 \cr } } \right| = 0} \right\},$$

then $$\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $$ is equal to :

If $$A = \left[ {\matrix{ 2 & { - 3} \cr { - 4} & 1 \cr } } \right]$$,

then adj(3A² + 12A) is equal to

If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1
x + ay + z = 1
ax + by + z = 0

has no solution, then S is :

Let A be a 3 $$ \times $$ 3 matrix such that A² $$-$$ 5A + 7I = 0

Statement - I :  

A^$$-$$1 = $${1 \over 7}$$ (5I $$-$$ A).

Statement - II :

The polynomial A³ $$-$$ 2A² $$-$$ 3A + I can be reduced to 5(A $$-$$ 4I).

Then :