## Find a Formula for a Linear Transformation

## Problem 36

If $L:\R^2 \to \R^3$ is a linear transformation such that

\begin{align*}

L\left( \begin{bmatrix}

1 \\

0

\end{bmatrix}\right)

=\begin{bmatrix}

1 \\

1 \\

2

\end{bmatrix}, \,\,\,\,

L\left( \begin{bmatrix}

1 \\

1

\end{bmatrix}\right)

=\begin{bmatrix}

2 \\

3 \\

2

\end{bmatrix}.

\end{align*}

then

**(a)** find $L\left( \begin{bmatrix}

1 \\

2

\end{bmatrix}\right)$, and

**(b)** find the formula for $L\left( \begin{bmatrix}

x \\

y

\end{bmatrix}\right)$.

If you think you can solve (b), then skip (a) and solve (b) first and use the result of (b) to answer (a).

(Part (a) is an exam problem of *Purdue University*)