Find the Standard Matrix of the Linear Transformation T $R ^ { 2 } \rightarrow R ^ { 2 }$

Multiple Choice

Find the standard matrix of the linear transformation T.
-T: $R ^ { 2 } \rightarrow R ^ { 2 }$ first performs a vertical shear that maps $\mathbf { e } _ { 1 }$ into $\mathbf { e } _ { 1 } + 3 \mathbf { e } _ { 2 }$ , but leaves the vector $\mathbf { e } _ { 2 }$ unchanged, then reflects the result through the horizontal $x _ { 1 }$ -axis.

A)
$\left[ \begin{array} { r r } - 1 & - 3 \\ 0 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { r r } 1 & 3 \\ 0 & - 1 \end{array} \right]$

C)
$\left[ \begin{array} { r r } 1 & 0 \\ - 3 & - 1 \end{array} \right]$

D)

$\left[ \begin{array} { r r } - 1 & 0 \\ 3 & - 1 \end{array} \right]$