MATH 3A Study Guide - Midterm Guide: Row Echelon Form, Invertible Matrix, Characteristic Polynomial
2
MATH 3A Full Course Notes
Verified Note
2 documents
Document Summary
Friday november 13, 5:00- 5:50pm november 13, 2015. Matrix is invertible if c (cid:54)= 1. (b) 0 by b). (c) [1, 3, 1]t (just multiply a 1. Exercise 2 (a) [1, 2, 1, 0, 0]t , [2, 3, 0, 1, 0]t , [3, 4, 0, 0, 1]t . Exercise 3 (a) characteristic polynomial is (2 )(2 )(1 ) (easy to compute). Hence eigenvalues are 2 and 1. (b) for 2: span([1, 0, 0]t , [0, 1, 3]t ). For 1: span([1, 0, 1/2]t ). (c) yes (answer not unique): Exercise 4 (a) false, if b (cid:54)= 0, then 0 is not in the solution set. (b) true. B is invertible if and only if bt is invertible.
