Let $$\vec{x} = \left\lbrack \begin{array}{c} a \\ b \end{array} \right\rbrack, \ \vec{v} = \left\lbrack \begin{array}{c} -6 \\ 1 \end{array} \right\rbrack, \ \mbox{ and } \ \vec{w} = \left\lbrack \begin{array}{c} -6 \\ 5 \end{array} \right\rbrack.$$ Let $T: {\mathbb R}^2 \rightarrow {\mathbb R}^2$ be a linear transformation defined by mapping every $\vec{x} = \left\lbrack \begin{array}{c} a \\ b \end{array} \right\rbrack$ to $a \vec{v} + b \vec{w}$. Find a matrix $A$ such that $T(\vec{x})=A\vec{x}$.

$A =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$