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**antman** Let L: $\displaystyle R^{2}->R^{2}$ be defined by $\displaystyle L(\begin{pmatrix}x\\y\end{pmatrix})=\begin{pmatrix }x+2y\\2x-y\end{pmatrix}$.

Let S be the natural basis for $\displaystyle R^{2}$ and let $\displaystyle T={\begin{pmatrix}-1\\2\end{pmatrix},\begin{pmatrix}2\\0\end{pmatrix} }$ be another basus for $\displaystyle R^{2}$. Find the matrix representing L with respect to:

a) S

b) S and T

c) T and S

d) T

e) Compute L$\displaystyle (\begin{pmatrix}1\\2\end{pmatrix})$ using the definition of L and also using the matrices obtained in (a), (b), (c) and (d).

Any help would be incredibly appreciated or an example of how a problenm like this is to be done.