4. Let $T$ be a map that sends the vector $(x, y, z)$ in $\mathbb{R}^3$ to $(x + 2y, y + 2z, z - 3x)$. In functional notation this is written:
$$T((x, y, z)) = (x + 2y, y + 2z, z - 3x).$$
(a) Find the image of the vector $(1, 2, 7)$, that is $T((1, 2, 7))$.
(b) Find $T((6, 3, 1))$
(c) Find a matrix $A$ that represents $T$, so that $T(\mathbf{v}) = A\mathbf{v}$ for all $\mathbf{v} \in \mathbb{R}^3$.
