Exercise 2

Decide if each map $h\colon\mathcal{M}_{2\!\times\!2}\to\mathbb{R}$ is linear.

• $h(\begin{pmatrix}a&b\\ c&d\end{pmatrix})=a+d$

• $h(\begin{pmatrix}a&b\\ c&d\end{pmatrix})=ad-bc$

• $h(\begin{pmatrix}a&b\\ c&d\end{pmatrix})=2a+3b+c-d$

• $h(\begin{pmatrix}a&b\\ c&d\end{pmatrix})=a^{2}+b^{2}$