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Exercise 3

Avg difficulty 3.0

Let $h$ be the linear map defined by this matrix on the domain $\mathcal{P}_{1}$ and codomain $\mathbb{R}^{2}$ with respect to the given bases.

H=\begin{pmatrix}2&1\\ 4&2\end{pmatrix}\quad B=\langle 1+x,x\rangle,\,D=\langle\begin{pmatrix}1\\ 1\end{pmatrix},\begin{pmatrix}1\\ 0\end{pmatrix}\rangle

What is the image under $h$ of the vector $\vec{v}=2x-1$ ?

Hefferon, Linear Algebra, Maps Between Spaces, Any Matrix Represents a Linear Map, Exercise 3

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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.