Exercise 1

Decide if each $h\colon\mathbb{R}^{3}\to\mathbb{R}^{2}$ is linear.

• (a)  $h(\begin{pmatrix}x\\ y\\ z\end{pmatrix})=\begin{pmatrix}x\\ x+y+z\end{pmatrix}$     (b)  $h(\begin{pmatrix}x\\ y\\ z\end{pmatrix})=\begin{pmatrix}0\\ 0\end{pmatrix}$     (c)  $h(\begin{pmatrix}x\\ y\\ z\end{pmatrix})=\begin{pmatrix}1\\ 1\end{pmatrix}$     (d)  $h(\begin{pmatrix}x\\ y\\ z\end{pmatrix})=\begin{pmatrix}2x+y\\ 3y-4z\end{pmatrix}$