Let $V$ be the plane with equation $x_1 - 2 x_2 + 3 x_3 =0$ in ${\mathbb R}^3$. The linear transformation $$T\left(\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}\right)= \left[\begin{array}{ccc} -5 &5 &5\cr -1 &1 &1\cr 1 &-1 &-1 \end{array}\right] \begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$$ maps $V$ into $V$ so, by restricting it to $V$, we may regard it as a linear transformation $\tilde T \colon V \to V$.

Find the matrix $A$ of the restricted map $\tilde T \colon V \to V$ with respect to the basis $\left\lbrace \left[\begin{array}{c} 2\cr 1\cr 0 \end{array}\right], \left[\begin{array}{c} -3\cr 0\cr 1 \end{array}\right] \right\rbrace.$

$A=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$