Www.tesd.net



Goal: Determine whether a matrix has an inverse. Solve systems using inverse matrices.

Thinking Skill: Gather and organize information and data.

Quick Review of Matrix Multiplication:

Multiply the following matrices.

a. [pic]=

b. [pic]

c. [pic]

d. [pic]

Think back to the beginning of the year…

What is the multiplicative inverse of:

a.) 3 b.) -7 c.)[pic]

When you multiply a number by its inverse, the result is always: _________

Finding the Multiplicative Inverse of a Matrix:

• Only possible with square matrices

• If A and B are inverse matrices then:

AB = I and BA = I, where I = Identity Matrix I = [pic]

• Inverse of matrix A is denoted by [pic]

Formula for Inverse

[pic] What does [pic] mean?

a.) A = [pic]

b.) B = [pic]

c.) C = [pic]

Solving Systems Using Inverse Matrices

a.) [pic]

Step 1: Rewrite as a MATRIX EQUATION:

Step 2: Solve for X:

b.) [pic]

c) [pic]

d) [pic]

Challenge Problem: Solve the following system using matrix equations:

[pic]

-----------------------

Date _________ Period_________

U3 D9: Matrix Inverses and Solving Systems

Step 1: Check the dimensions. Is it possible to multiply?

Step 2: Multiply Row x Column

Coefficient Unknown Constant

Matrix Matrix Matrix

A • X = B

A matrix with a determinant of

________________________

does not have an inverse!

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download