Can anyone walk me through the steps to complete this problem? I am unsure of where to start to solve the problem. I get that the resulting matrix $A$ should be a $2 \times2$ matrix, should I be finding another vector in the basis to find $BAB^{-1}$?
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 $T(x)= \displaystyle\left[\begin{array}{ccc} -6 &-12 &0 \cr -2 &-2 &1 \cr -1 &2 &2 \cr \end{array}\right] x$ with respect to the basis $\displaystyle\left[\begin{array}{c} 4 \cr 1 \cr 0 \cr \end{array}\right]$ , $\displaystyle\left[\begin{array}{c} -2 \cr 0 \cr 1 \cr \end{array}\right]$