# Science:Math Exam Resources/Courses/MATH152/April 2015/Question A 16/Solution 1

First, note that ${\displaystyle A{\begin{bmatrix}1\\0\end{bmatrix}}}$ and ${\displaystyle A{\begin{bmatrix}0\\1\end{bmatrix}}}$ are the first and second columns of ${\displaystyle A}$, respectively.
The latter is given, and we notice that ${\displaystyle A{\begin{bmatrix}1\\0\end{bmatrix}}=A\left({\begin{bmatrix}1\\1\end{bmatrix}}-{\begin{bmatrix}0\\1\end{bmatrix}}\right)=A{\begin{bmatrix}1\\1\end{bmatrix}}-A{\begin{bmatrix}0\\1\end{bmatrix}}={\begin{bmatrix}5\\4\end{bmatrix}}-{\begin{bmatrix}2\\2\end{bmatrix}}={\begin{bmatrix}3\\2\end{bmatrix}},}$ so
${\displaystyle A=\color {blue}{\begin{bmatrix}3&2\\2&2\end{bmatrix}}.}$