Let $L$:$R^2{R}^2$ be a linear transformation defined by

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$L(\left[\begin{array}{c}1\\ 0\end{array}\right])=\left[\begin{array}{c}1\\ -2\end{array}\right],L(\left[\begin{array}{c}0\\ 1\end{array}\right])=\left[\begin{array}{c}-1\\ 5\end{array}\right]$

a$)$ Let $A$ be the representation of $L$ with respect to the standard basis $S$ for $R^2$ Find the entries of $A.$

$a_{11}=$

$a_{12}=$

$a_{21}=$

$a_{22}=$

b$)$ If $L(\left[\begin{array}{c}3\\ -4\end{array}\right])=aL(\left[\begin{array}{c}1\\ 0\end{array}\right])+bL(\left[\begin{array}{c}0\\ 1\end{array}\right])=\left[\begin{array}{c}c\\ d\end{array}\right].$ Then

$a=$

$b=$

$c=$

$d=$