What you will learn 1. What an identity matrix is

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

Homework Page 227, 14-18 even, 34, 36, 38, 44, 46 Objective: 4.4 Identity and Inverse Matrices