MATH136 Chapter Notes - Chapter 139-174: Laplace Expansion, Triangular Matrix, Adjugate Matrix

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Dan Wolczuk

Document Summary

Let a be an m n matrix. If b is an n m matrix such that ab = im, then b is called a right inverse of a. If c is an n m matrix such that ca = in, then c is called a left inverse of a. If a is an m n matrix with m > n, then a cannot have a right inverse. If a is an m n matrix with m < n, then a cannot have a left inverse. An n n matrix is called a square matrix. If a, b, and c are n n matrices such that ab = i = ca, then b = c. If b is a matrix such that ab = i = ba, the b is called the inverse of a. We write b = a 1 and we say that a is invertible.