Extra Credit Writing Assignment 4
The draft has to be submitted on Monday, November 17 or Wednesday,
November 19. The final version is due on Monday, December 1.
1. (1 pts.) Problem 20 (a), page 277.
2. (1 pts.) Problem 26, page 309.
3. (1 pts.) Problem 27, page 309.
4. (2 pts.) Let Aand Bbe two n×nmatrices such that AB =BA.
(a) Show that if xis an eigenvector of Athen either Bx=0or Bxis an
eigenvector of A.
(b) Show that if Ahas ndistinct eigenvalues then Bhas the same eigenvec-
tors as A. Moreover, both Aand Bcan be diagonalized, and if A=P DP −1
with an invertible matrix Pand a diagonal matrix D, then B=PFP−1
with the same Pand a diagonal matrix F.
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