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Exercise 19

Avg difficulty 3.0

Describe geometrically the action on $\mathbb{R}^{2}$ of the map represented with respect to the standard bases ${\cal E}_{2},{\cal E}_{2}$ by this matrix.

\begin{pmatrix}3&0\\ 0&2\end{pmatrix}

Do the same for these.

\begin{pmatrix}1&0\\ 0&0\end{pmatrix}\quad\begin{pmatrix}0&1\\ 1&0\end{pmatrix}\quad\begin{pmatrix}1&3\\ 0&1\end{pmatrix}

Hefferon, Linear Algebra, Maps Between Spaces, Any Matrix Represents a Linear Map, Exercise 19

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