how to find matrix A from complete solution to Ax=b

Question

I am trying to solve a problem. I was stuck.Any help is appreciated.

The complete solution to $Ax=\left[\begin{array}[c]{rr}1 \\3 \end{array}\right]$ is $ x= \left[\begin{array}[c]{rr}1\\0\end{array}\right]+ c \left[\begin{array}[c]{rr}0\\1\end{array}\right].$ Find Matrix A.

Answer 1

Hint: Write up $A=\pmatrix{a&b\\c&d}$ and use the deduced equations $$\begin{align} A\pmatrix{1\\0}\ &=\ \pmatrix{1\\3} \\[3pt] A\pmatrix{0\\1}\ &=\ \pmatrix{0\\0} \,. \end{align}$$