1. What you will learn 1. What an identity matrix is
2. How to find the inverse of a 2x2 and other size matrices
3. How to decode messages using inverse matrices

2. Identity Matrix
Any number multiplied by 1 is the same number (multiplicative identity). What is the “multiplicative identity” for a matrix?
An identity matrix for any matrix is the matrix that has 1’s on the main diagonal and 0’s elsewhere. e.g.
Identity for 3x3
Identity for 2x2
Objective: 4.4 Identity and Inverse Matrices

3. Inverse Matrices What happens when I multiply ½ by 2?
What do you suppose would happen if I multiplied any matrix by its inverse?
Let’s see: Matrix B is the inverse of Matrix A. Find AB:
We refer to the inverse of A as A-1.
Objective: 4.4 Identity and Inverse Matrices

4. How Do You Get the Inverse of a Matrix?
Glad you asked!
The inverse of Matrix A= is:
Provided the determinant of A is not zero.
Objective: 4.4 Identity and Inverse Matrices

5. Example Find the inverse of A =
Objective: 4.4 Identity and Inverse Matrices

6. On A Calculator Find the inverse of A =
Objective: 4.4 Identity and Inverse Matrices

7. Finding the Inverse of a 3x3 Matrix
We will only do this on a calculator! Yeah!
Example: Find the inverse of A:
Objective: 4.4 Identity and Inverse Matrices

8. Using Inverse Matrices
Encoding and decoding messages.
Number the letters A through Z, 1 through 26.
Let 0 = a blank space.
Example: Convert “Get Help” to a coded set of 1 x 2 matrices.
G E T _ H E L P
Objective: 4.4 Identity and Inverse Matrices

9. Encoding
Use the converted matrices from the previous “get help” example.
Use A = to encode the matrices.
[ 7 5 ]
[20, 0]
[8, 5]
[12, 16]
Objective: 4.4 Identity and Inverse Matrices

10. The Encoded Message The encoded message should be:
9, 11, 40, 60, 11, 14, 8, 4
To decode, find the inverse of the coding matrix:
Multiply each of the 1 x 2 matrices by the inverse to decode the message.
Objective: 4.4 Identity and Inverse Matrices

11. Decoding (continued) 9, 11, 40, 60, 11, 14, 8, 4 and inverse:
Objective: 4.4 Identity and Inverse Matrices

12. You Try Use the inverse of A = to decode the following:
-4, -1, -12, 7, -18, 18, 11, -20, -12, 7, 42, -63, -16, 16
Objective: 4.4 Identity and Inverse Matrices

13. Homework
Page 227, even, 34, 36, 38, 44, 46
Objective: 4.4 Identity and Inverse Matrices