MATH 21B Study Guide - Midterm Guide: Orthogonal Matrix, Rotation Matrix, Symmetric Matrix
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Tth 11:30 alison miller: please ll in your name and mark your section, try to answer each question on the same page as the question is asked. If needed, use the back or the next empty page for work. If you need additional paper, write your name on it: do not detach pages from this exam packet or un- staple the packet, please write neatly and except for problems 1-3, give details. Answers which are illegible for the grader can not be given credit: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. There is a real diagonalizable 3 3 matrix for which the algebraic multiplicity of an eigenvalue = 2 is larger than 1. Two symmetric not-invertible 3 3 matrices a, b are similar if their trace agrees. Every orthogonal 5 5 matrix has a real eigenvalue.