MATH125 Lecture Notes - Lecture 19: Identity Matrix, Invertible Matrix, Elementary Matrix

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

A square matrix a of size n n is invertible if there exists a matrix c of the same size n n such that ac = ca = in. In this case we say that a is invertible and that c is an inverse of a and we denote it by c = a 1. It is not true that every square matrix is invertible. Later we nd a criterion when a square matrix is invertible. If a has inverse then it is unique. B = b in = b(ac) = (ba)c = inc = c. 3 7 ] , c = [ 7 5. Verify that c is the inverse of a. We must check that ac = ca = i2. The following theorem says that if we know that the coe cient ma- trix of a linear system has inverse then we can easily produce its solu- tion.