Mat 150 – Class #24

Objectives

Find the inverse of a matrix Find matrix inverses with technology Solve matrix equations Solve matrix equations with technology

Inverse MatricesTwo square matrices, A and B, are called inverses of each other if

AB = I and BA = Iwhere I is the identity matrix. We denote this by B = A–1 and A = B–1.

Example

Solve that A and B are inverses matrices if

Solution

1 0.6 0.2 2 2 1

0 0.4 0.2 and 1 3 1

1 0.4 0.8 2 1 2

A B

Examples

a) Find the inverse of Solution

b) If , solve for .

2 1 2

1 0 1

4 2 3

A

Example

Solve the system

by writing a matrix equation and using an inverse matrix.Solution

2 2 5

2

4 2 3 4

x y z

x z

x y z

Example

Ace Trucking Company has an order for delivery of three products: A, B, and C. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?

Assignment

Pg.544-548 #1-23 odd #25 #30

Quiz Monday November 24 which will be over lectures from Class 21 thru Class 23

Some Key Concepts:

• Solve systems of linear equations in three variables using left-to-right elimination

• Find solutions of dependent systems

• Determine when a system of equations is inconsistent

• Represent systems of equations with matrices

• Identify an identity matrix

• Form an augmented matrix

• Identify a coefficient matrix

• Reduce a matrix with row operations

• Reduce a matrix to its row-echelon form

• Add two matrices

• Subtract two matrices

• Multiply a matrix by a constant

• Multiply two matrices