Due Oct 20 Wednesday @ 11:59pm
Submit a PDF (scanned/photographed from handwritten solutions, or converted from RMarkdown or Jupyter Notebook) to Gracescope on CCLE.
BV exercises: 7.6, 7.7, 7.13, 8.2, 8.4, 8.6, 8.14.
For 7.6 and 7.7, you can use the definition of incidence matrix either in the BV book or in lecture notes.
Q1. Show that if $\mathcal{S}_1$ and $\mathcal{S}_2$ are two vector spaces of same order, then their intersection $\mathcal{S}_1 \cap \mathcal{S}_2$ is a vector space.
Q2. Show by a counter-example that if $\mathcal{S}_1$ and $\mathcal{S}_2$ are two vector spaces of same order, then their union $\mathcal{S}_1 \cup \mathcal{S}_2$ is not necessarily a vector space.