Midterm review

  • Q1.6. Showed $\text{rank}(AB) \le \text{rank}(A)$ from Q1.5 but could not show $\text{rank}(AB) \le \text{rank}(B)$ from $\mathcal{R}(AB) \subset \mathcal{R}(B)$.

  • Q2.5. Found $\text{rank}(A+B) < \text{rank}(A) + \text{rank}(B)$, but could not find $\text{rank}(A+B) = \text{rank}(A) + \text{rank}(B)$.

  • Q4.3. $Axy’$ flops.

  • Q4.4. $AD$ flops ($D$ is diagonal).

  • Q5. Did not consider any vector (say, $z$) in S (just assumed $x$ and $y$ in $S^\perp$).

  • Q10.2. Middle element of an anti-symmetric vector was not 0.

  • Q10.8. No time or $\text{dim}(S_1) = \text{dim}(S_2) = n$ for some reason. Those who noticed $\text{dim}(S_1) + \text{dim}(S_2) = n$ all made it (they all gave both solutions when n is even and odd).

Today

  • Orthogonal projection.