MATH 3A Study Guide - Midterm Guide: Gaussian Elimination, Surjective Function, Elementary Matrix

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 3A
• Professor: All

Document Summary

Solution: we compute the determinant and nd when it is zero. Expanding across the top row gives: (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) a. 1 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = a (a 1 0 1) + 1 ( 1 1 a 0) = a2 1. So the matrix is invertible unless a = 1. Math 54: label the following statements as either true or false. 2-dimensional. (h) if a and b are n n matrices and ab is invertible, then ba must be invertible too. For example, using row reduction you can express a as a product of elementary matrices, and then it su ces to verify that det et = det e where e is an elementary matrix: is false. Either we also need to require that ba = i, or we need to require that a and b are (cid:20) 1 0 0. Otherwise, a = and b : is true.