The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is

The value of the determinant $$\left| {\matrix{ 1 & 3 & 2 \cr 4 & 1 & 1 \cr 2 & 1 & 3 \cr } } \right|$$ is

The determinant $$\left| {\matrix{ {1 + b} & b & 1 \cr b & {1 + b} & 1 \cr 1 & {2b} & 1 \cr } } \right|$$ equals to

If $$A$$ is square symmetric real valued matrix of dimension $$2n$$, then the eigen values of $$A$$ are