Let $$A = \left[\begin{array}{cc} 2 &1\cr 5 &2 \end{array}\right] \ \mbox{ and } \ \vec{b} = \left[\begin{array}{c} -1\cr -3 \end{array}\right].$$ Define the linear transformation $T: {\mathbb R}^2 \rightarrow {\mathbb R}^2$ by $T(\vec{x}) = A\vec{x}$. Find a vector $\vec{x}$ whose image under $T$ is $\vec{b}$.

$\vec{x} =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$.
Is the vector $\vec{x}$ unique? choose unique not unique