Resources for Midterm 2, Mathematics 54, Spring 2012

Old midterms for practice:

Please ignore all "least squares" and "complex numbers" problems (Sections 5.5 and 6.5 in the text). But I will ask you about the Gram-Schmidt process (Section 6.4).

Complex numbers will not be on this exam, nor on the final. The least squares methods will be on the final exam.

Practice Exam 1 (Tabrizian)   (also ignore 8)   Answer Key

Practice Exam 3 (Bergman)   (also ignore 2c)   Answer Key

List of definitions which may appear on the midterm:

Do not memorize definitions without understanding them!

Definition of coordinates, p.234

Definition of dimension, p.245

Definition of rank, p.253

Definition of change-of-coordinate matrix, p.261

Definition of eigenvalues and eigenvectors, p.271

Definition of the characteristic equation, p.281

Definition of similarity (p. 282) and of diagonalizability (p. 288)

Defintion of a matrix relative to coordinates, p.296

Definitions of length, distance, orthogonality, Section 6.1

Definition of orthogonal projection, p.326

List of proofs which may appear on the midterm:

Chapter 4, Theorem 7 (proof on p.234)

Chapter 4, Theorem 8 (proof on p.238)

Chapter 4, Theorems 9,10 (proofs on pp.244,245)

Chapter 4, Theorem 14 (proof on 253 or a different presentation in lecture)

Chapter 5, Theorem 2 (proof on p.275)

Chapter 5, Theorem 4 (proof on p.283 or a different presentation in lecture)

Chapter 5, Theorem 5 (proof on p.289)