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Exercise 6

Avg difficulty 3.0

Consider a homomorphism $h\colon\mathbb{R}^{2}\to\mathbb{R}^{2}$ represented with respect to the standard bases ${\cal E}_{2},{\cal E}_{2}$ by this matrix.

\begin{pmatrix}1&3\\ 2&4\end{pmatrix}

Find the image under $h$ of each vector.

(a) $\begin{pmatrix}2\\ 3\end{pmatrix}$ (b) $\begin{pmatrix}0\\ 1\end{pmatrix}$ (c) $\begin{pmatrix}-1\\ 1\end{pmatrix}$

Hefferon, Linear Algebra, Maps Between Spaces, Any Matrix Represents a Linear Map, Exercise 6

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