If $$A = {1 \over 2}\left[ {\matrix{ 1 & {\sqrt 3 } \cr { - \sqrt 3 } & 1 \cr } } \right]$$, then :

Let $$S$$ denote the set of all real values of $$\lambda$$ such that the system of equations

$$\lambda x+y+z=1$$

$$x+\lambda y+z=1$$

$$x+y+\lambda z=1$$

is inconsistent, then $$\sum_\limits{\lambda \in S}\left(|\lambda|^{2}+|\lambda|\right)$$ is equal to

For the system of linear equations

$$x+y+z=6$$

$$\alpha x+\beta y+7 z=3$$

$$x+2 y+3 z=14$$

which of the following is NOT true ?

Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 1} \cr 0 & {12} & { - 3} \cr } } \right)$$. Then the sum of the diagonal elements of the matrix $${(A + I)^{11}}$$ is equal to :