$\begin{array}{rl}{x}^{\prime}& =4x+2y+14\\ {y}^{\prime}& =2x+7y+42\end{array}$

Find the coordinates of the invariant point of $\mathbf{\text{T}}$. Hence express $\mathbf{\text{T}}$ in the form

$\left(\begin{array}{c}{x}^{\prime}\\ {y}^{\prime}+k\end{array}\right)=\mathbf{\text{A}}\left(\begin{array}{c}x\\ y+k\end{array}\right)$

where $k$ is a positive integer and $\mathbf{\text{A}}$ is a $2\times 2$ matrix.