Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Systems and Matrices
Subtopic: Matrix Inversion

Overview

To solve an algebraic equation such as 5x=12 we invert the 5 and multiply both sides by 1/5 to isolate the x. Today we do a similar process except with matrices. Matrix inversion is somewhat analogous to matrix division and will enable us to solve matrix equations. Practice working the problems algebraically and electronically. Technology comes in particularly handy when finding the inverse of a large square matrix. See the class calendar for links to my Calculator Guide to Inverse Matrices.

By the end of this section you should be able to solve a square consistent system of linear equations by any of the following methods:

• Algebraically by substitution or elimination methods
• Gaussian elimination to transform to row echelon form (REF) followed by back substitution
• Gauss-Jordan elimination to transform to reduced row echelon form (RREF)
• Matrix equation method (

using the inverse matrix)

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 5.5.1 Check if two given matrices are inverses of one another
• 5.5.2 Recognize a multiplicative identity matrix and a multiplicative inverse matrix
• 5.5.3 Find an inverse matrix using the AI->IA-1 method
• 5.5.4 Use the shortcut method to finding the inverse of a 2x2 matrix (note the shortcut only works for 2x2's)
• 5.5.5 Know that if the determinant of a square matrix is zero is does not have an inverse
• 5.5.6 Solve a matrix equation AX=B by the matrix equation method (AX=B -> X=A-1B)

Terminology

Terms you should be able to define: multiplicative identity matrix (a.k.a. identity matrix), multiplicative inverse matrix (a.k.a. inverse matrix), invertible, non-invertible

rev. 2020-11-29