I am new to linear transormations and I can do the $\Bbb R^m \to \Bbb R^n$ tranformations, however I came up to this question and im confused. I'd be grateful if any of you could guide me how to start it please?
Let $g : \Bbb R^3 \to \Bbb R^3$ be the linear transformation satisfying $g \left( \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} \right) = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, \ g \left( \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} \right) = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$ and $g \left( \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix} \right) = \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}$.
Find a $3 \times 3$ matrix $A$ such that $g(x) = AxT$ for all $x \in \Bbb R^3$