Chapter 4 Section 5 and 6
Finding and Using Inverses
Algebra 2 Notes
February 26, 2009
Warm-Ups

Solve each matrix equation for X:

Explain how to determine whether two matrices
can be multiplied and what the dimensions of the
product matrix will be.
Square Matrix

Look on Page 199:
◦ What is the definition of a square matrix??
(2 X 2)
(3 X 3)
etc…..
Review: Identity Matrix

Look on Page 199:
◦ What is the definition of a multiplicative
identity matrix?
etc…
Inverse Matrices

Show that B is the multiplicative inverse
of A:
◦ If B is an inverse of A then AB = I
Determinants

A determinant will determine if a matrix has an
inverse
◦ If the determinant = 0 then that matrix has NO
INVERSE!
det A = ad – bc

Find the following determinants:
Solving Matrix Equations

Solve the following equation for X:
Matrix A
Matrix B
Solving a System of Equations

System of equations:

Matrix Equation:
Coefficient
Matrix A
Variable
Matrix X
Constant
Matrix B
Solving a System of Equations

Solve the following system of equations
using inverse matrices:
Homework #31
Page 203 #1*, 14-16**, 22, 25***
• *Do #1 by hand!
• **Use determinants to determine if it has a
inverse, then use the calculator to find the
actual inverse for #14-16
• ***Refer to Example 5 on pg 202 for #25
Page 217 #7, 8, 13, 14, 16, 23, 24, 30