This WeekÕs Homework: No homework (turn in last week's HW though!). The final exam was handed out on last Friday. Comments will be posted on this web page. Office ours will be by appointment (e-mail me) from here on out.

Proposed Topics For this Week: Proof of Spectral theorem on Monday. (OOOOPS we only got to Schur's theorem. If any one would like for us to meet and discuss the spectral theorem (which is supper neato!), e-mail me good times.)

Exam Comments

1.

2(e) is not trivial. Notice that for any matrix ch(B) is another matrix while $\det(A- BI)$ is a scalar, so they are not the same type of object (let alone equal!).

2.

1(f) should read "Let $A \in M_{2 \times 2} ({\bf Q})$. Prove that if A has an eigenvalue with algebraic multiplicty two then A's eigenvalues and eigenvectors can be made out of rational numbers." (eigenvector has been replaced with eigenvalue.)