Matrices Practice Test

If $$A = \begin{pmatrix} 5 & 2 \\ 2 & 1 \end{pmatrix}$$ and $$AX = \begin{pmatrix} 3 \\ 1 \end{pmatrix}$$, what is the matrix $$X$$?

Let $$u_k$$ and $$s_k$$ be the populations of the urban center and suburbs in year $$k$$, respectively. Let the state vector be $$\vec{v}k = \begin{pmatrix} u_k \ s_k \end{pmatrix}$$. Which matrix $$T$$ models this yearly transition, such that $$\vec{v}{k+1} = T\vec{v}_k$$?