1. Chapter 4 Section 5 and 6 Finding and Using Inverses Algebra 2 Notes February 26, 2009

2. 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.

3. Square Matrix Look on Page 199: ◦ What is the definition of a square matrix?? (2 X 2) (3 X 3) etc…..

4. Review: Identity Matrix Look on Page 199: ◦ What is the definition of a multiplicative identity matrix? etc…

5. Inverse Matrices Show that B is the multiplicative inverse of A: ◦ If B is an inverse of A then AB = I

6. 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:

7. Solving Matrix Equations Solve the following equation for X: Matrix AMatrix B

8. Solving a System of Equations System of equations: Matrix Equation: Coefficient Matrix A Variable Matrix X Constant Matrix B

9. Solving a System of Equations Solve the following system of equations using inverse matrices:

10. 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