MATH 125 Study Guide - Final Guide: Row Echelon Form, Invertible Matrix, Elementary Matrix
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Notes: some of the solutions here are incomplete (their main purpose is to enable you to check your own answers). In particular, row reduction of matrices and determinant calculations are omitted for the most part. In your exam, however, you should show all your work, and give suitable justi cation for your answers. Note also that there are often multiple ways to solve a particular problem; in these solutions, we typically just give one approach. 1: de ne what it means for an n n matrix to be invertible, find the inverse (if it exists) of the matrix. 2 1 1: for which value(s) of a is the matrix. 2 (the right side of the partitioned matrix). (c) let b be the given matrix. Then: (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (r3 2r1) (expand along 1st column) det(b) =(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) Hence b is invertible if and only if 2a 6= 0, i. e. , if and only if a 6= 0: let a = .
