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Exercise 6

Avg difficulty 3.0

Let $h\colon\mathbb{R}^{2}\to\mathcal{M}_{2\!\times\!2}$ be the linear transformation with this action.

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

What is its effect on the general vector with entries $x$ and $y$ ?

Hefferon, Linear Algebra, Maps Between Spaces, Representing Linear Maps with Matrices, Exercise 6

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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.