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Exercise 7

Avg difficulty 3.0

Assume that $h\colon\mathbb{R}^{2}\to\mathbb{R}^{3}$ is determined by this action.

\begin{pmatrix}1\\ 0\end{pmatrix}\mapsto\begin{pmatrix}2\\ 2\\ 0\end{pmatrix}\qquad\begin{pmatrix}0\\ 1\end{pmatrix}\mapsto\begin{pmatrix}0\\ 1\\ -1\end{pmatrix}

Using the standard bases, find

the matrix representing this map;
a general formula for $h(\vec{v})$ .

Hefferon, Linear Algebra, Maps Between Spaces, Representing Linear Maps with Matrices, Exercise 7

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.