Suppose that $T$ is a linear transformation such that $$T\left( \left[\begin{array}{c} 1\cr 0\cr 0 \end{array}\right] \right) = \left[\begin{array}{c} -6 \end{array}\right], \ \ \ \ T\left( \left[\begin{array}{c} 0\cr 1\cr 0 \end{array}\right] \right) = \left[\begin{array}{c} 1 \end{array}\right], \ \ \ \ T\left( \left[\begin{array}{c} 0\cr 0\cr 1 \end{array}\right] \right) = \left[\begin{array}{c} -6 \end{array}\right].$$ Write $T$ as a matrix transformation.

For any $\vec{v} \in \mathbb{R}^3$, the linear transformation $T$ is given by $T( \vec v ) =$ $\left[\Rule{0pt}{1.2em}{0pt}\right.$$\left]\Rule{0pt}{1.2em}{0pt}\right.$ $\vec{v}$.