Problem 1 $\mathcal{R} \subseteq \mathcal{S}$ iff $\mathcal{S}^\perp \subseteq \mathcal{R}^\perp$
Problem 2 $(\mathcal{R} \cap \mathcal{S})^\perp = \mathcal{R}^\perp+\mathcal{S}^\perp$
What I Have Done
These two problems seem to be pretty fundamental but I failed to find materials that could help me.
I have proved something similar to the second problem, which is $(\mathcal{R} + \mathcal{S})^\perp = \mathcal{R}^\perp \cap \mathcal{S}^\perp$. But I could not do similar things that I did when I proved this similar problem.
What is more, could you recommend a comprehensive book on matrix analysis (hopefully the materials are detailed and contain some working examples). The textbook I use now seems to be too concise and sometimes very difficult to understand the topics covered.
Thank you in advance, I do appreciate your help.
