Answer
$A=\begin{bmatrix}-2&7\\5&-3\end{bmatrix}$
Work Step by Step
Let's use the notation $A=\begin{bmatrix}\mathbf{a_{1}}&\mathbf{a_{2}}\end{bmatrix}$. Then we want vectors $\mathbf{a_{1}}, \mathbf{a_{2}}$ such that the following holds true:
$A\mathbf{x}=\begin{bmatrix}\mathbf{a_{1}}&\mathbf{a_{2}}\end{bmatrix}\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}=x_{1}\mathbf{a_{1}}+x_{2}\mathbf{a_{2}}=x_{1}\mathbf{v_{1}}+x_{2}\mathbf{v_{2}}$.
But that simply means $\mathbf{a_{1}}=\mathbf{v_{1}}$ and $\mathbf{a_{2}}=\mathbf{v_{2}}$.
