INTRODUCTORY LINEAR ALGEBRA MATRIX INVERSES AND DETERMINANTS EXAM STUDY GUIDE 2024

Matrix inverses are analogous to the multiplicative inverse (or reciprocal) in the number system. In the number system, the multiplicative inverse, if it exists, is unique. Indeed, the matrix inverse, if it exists, is also unique similarly, as shown in the following proposition. is invertible and its inverse is since (it implies that the matrix product in another order is also by the invertible matrix theorem) if matrices and are invertible, is also invertible if matrices and are non-invertible, is also non-invertible if matrices and are invertible, and are also invertible if matrices and are non-invertible, is also non-invertible Matrix inverse can be used to solve SLE, as follows: Then, we will define the elementary matrix, which is closely related to EROs, and is important for the proof of results related to EROs.