Final Exam — Supplemental Review Problems

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True or False

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Work-out problems

Problem 1 — Transposition in different bases

Problem 2 — A polynomial map between ordered bases

Problem 3 — Reading a matrix in a nonstandard basis

Problem 4 — Eigenvectors of a polynomial operator

Problem 5 — Expansion in an orthonormal basis

Problem 6 — Vectors orthogonal to two given vectors

Problem 7 — Polynomial orthogonality

Problem 8 — Orthogonal and orthonormal sets

Problem 9 — Recovering a basis from a change-of-coordinates matrix