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# Chapter 8.4 - Systems of Linear Equations - Matrix Inverses

# Khan Academy - Inverse of 3-by-3 Matrix

# Khan Academy - Inverse of a 2-by-2 Matrix

# Khan Academy - Matrix Inverse Part 1

# Systems of Linear Equations - Matrix Inverse

## Overview

**TMM 002 PRECALCULUS** (Revised March 21, 2017)

**3. Equations and Inequalities:**

** 3a**. Recognize function families as they appear in equations and inequalities and choose an appropriate solution methodology for a particular equation or inequality, as well as communicate reasons for that choice.*

# Inverse of a Matrix

Recall that a simple linear equation of the form ** ax = b** has the solution

**,**

*x*=*b/a*= a^{-1}.b

*a ≠*0.As noted in earlier modules, a system of linear equations can be written as ** AX = B**, where

**and**

*A***are known matrices and**

*B***is the variable matrix. Note that this equation resembles a simple linear equation. The question is does the solution look like**

*X***? If so, what is**

*X*=*A*^{-1}. B**and how to find it?**

*A*^{-1}In this module we will learn about matrix inverse and use the same, if it exists, to find the solution to a system of linear equations.

**Review: **Augmented matrices and Gauss-Jordan Elimination method.

**Learning Objectives: **

- Square matrix, singular and non-singular matrices
- Identify matrix
- Inverse of a non-singular matrix
- Use the inverse, when it exists, to find the solution to a system of linear equations.