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

Why is this linear:
$$h\left(\begin{bmatrix}
x\\ y\\ z
\end{bmatrix}\right)=\begin{bmatrix}
0\\ 0
\end{bmatrix}$$
but this is not linear:
$$h\left(\begin{bmatrix}
x\\ y\\ z
\end{bmatrix}\right)=\begin{bmatrix}
1\\ 1
\end{bmatrix}$$