Answer
$A=\begin{bmatrix} 0 & -1 \\ 1 & 2\\3 &-4 \end{bmatrix}$
Work Step by Step
We have:
$A=T( \begin{bmatrix} x\\ y \end{bmatrix} )=\begin{bmatrix} -y\\x+2y\\ 3x-4y \end{bmatrix}\\=\begin{bmatrix} 0\\x\\ 3x \end{bmatrix}+\begin{bmatrix} -y\\2y\\ -4y \end{bmatrix}\\=\begin{bmatrix} 0 & -1 \\ 1 & 2\\3 &-4 \end{bmatrix}$
Thus, the required standard matrix of the linear transformation is: $A=\begin{bmatrix} 0 & -1 \\ 1 & 2\\3 &-4 \end{bmatrix}$
