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)
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