Let V be the plane with equation... Let $V$ be the plane with equation $x_1 - 4 x_2 - 2 x_3 =0$ in $\mathbb{R}^3$. Find the matrix $A$ of the linear transformation 
$T(x)= \begin{bmatrix} 4&amp; 2 &amp; -8 \\ 2 &amp; 1&amp; -1 \\ -2&amp; -1&amp; -2\end{bmatrix} x$ with respect to the basis $\{\begin{bmatrix} 4 \\ 1 \\ 0\end{bmatrix}, \begin{bmatrix} 2 \\ 0 \\ 1\end{bmatrix}\}$

Note: $T(x)$ is a 3x3 matrix and the basis are 3x1 matrices
Figure out how $T$ acts on the basis vectors $v_1 = (4,1,0)$ and $v_2 = (2,0,1)$.
The vector $T(v_1)$ should be a linear combination of $v_1$ and $v_2$. Find $a$ and $b$ with $T(v_1) = av_1 + bv_2$.
Similarly, write $T(v_2) = cv_1 + dv_2$.
The matrix $A$ is:


$$\left(\begin{array}{cc} a &amp; c \\ b &amp; d \end{array}\right)$$

Edit: corrected order of variables in matrix
Let $V$ be the plane with equation $x_1 - 4 x_2 - 2 x_3 =0$ in $\mathbb{R}^3$. Find the matrix $A$ of the linear transformation 
$T(x)= \begin{bmatrix} 4&amp; 2 &amp; -8 \\ 2 &amp; 1&amp; -1 \\ -2&amp; -1&amp; -2\end{bmatrix} x$ with respect to the basis $\{\begin{bmatrix} 4 \\ 1 \\ 0\end{bmatrix}, \begin{bmatrix} 2 \\ 0 \\ 1\end{bmatrix}\}$

Note: $T(x)$ is a 3x3 matrix and the basis are 3x1 matrices