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 _______.

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 ________.

Which one of the following statements is NOT true for a square matrix $$A$$?

The system of linear equations $$\left( {\matrix{ 2 & 1 & 3 \cr 3 & 0 & 1 \cr 1 & 2 & 5 \cr } } \right)\left( {\matrix{ a \cr b \cr c \cr } } \right) = \left( {\matrix{ 5 \cr { - 4} \cr {14} \cr } } \right)$$ has