The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 9 & 7 & {13} \cr { - 6} & { - 4} & { - 9 + x} \cr } } \right]$$ has zero as an eigen value is __________.

Let $${M^4} = {\rm I}$$ (where $${\rm I}$$ denotes the identity matrix) and $$M \ne {\rm I},\,\,{M^2} \ne {\rm I}$$ and $${M^3} \ne {\rm I}$$. Then, for any natural number $$k, $$ $${M^{ - 1}}$$ equals:

The value of $$'P'$$ such that the vector $$\left[ {\matrix{ 1 \cr 2 \cr 3 \cr } } \right]$$ is an eigenvector of the matrix $$\left[ {\matrix{ 4 & 1 & 2 \cr P & 2 & 1 \cr {14} & { - 4} & {10} \cr } } \right]$$ is ________.

Consider system of linear equations : $$$x-2y+3z=-1$$$ $$$x-3y+4z=1$$$ and $$$-2x+4y-6z=k,$$$

The value of $$'k'$$ for which the system has infinitely many solutions is _______.