chapter 4 section 5 and 6 finding and using inverses algebra 2 notes february 26, 2009

Chapter 4 Section 5 and 6Finding and Using InversesAlgebra 2 NotesFebruary 26, 2009

Warm-UpsSolve 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 MatrixLook on Page 199:

◦What is the definition of a square matrix??

(2 X 2) (3 X 3) etc…..

Review: Identity MatrixLook on Page 199:

◦What is the definition of a multiplicative identity matrix?

etc…

Inverse MatricesShow that B is the multiplicative

inverse of A:◦If B is an inverse of A then AB = I

DeterminantsA determinant will determine if a

matrix has an inverse◦ If the determinant = 0 then that matrix has

NO INVERSE!

det A = ad – bcFind the following determinants:

Solving Matrix Equations

Solve the following equation for X:

Matrix A

Matrix B

Solving a System of EquationsSystem of equations:

Matrix Equation:

Coefficient Matrix A

Variable Matrix X

Constant Matrix B

Solving a System of EquationsSolve the following system of

equations using inverse matrices:

Homework #31Page 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