Today, you will be able to: Algebra 2 Wednesday 12-3-14 Warm ups Complete Slide below Discussion/Notes/Guided Practice 4.7 Identity and Inverse Matrices Assignment: A#4.7 page 213 #9-21 all Today, you will be able to: Define new vocabulary: identity matrix; inverse Determine whether two matrices are inverses Find the inverse of a 2 x 2 matrix Chapter 4 Test Tuesday, 12/9 Success Criteria: Q&A Guided Practice Homework

Prior Knowledge Self-Evaluation – Know vs. Need to Know Define new vocabulary: identity matrix; inverse Determine whether two matrices are inverses Find the inverse of a 2 x 2 matrix

Intro to Inverse Matrices

Identity Matrix: a square matrix that, when multiplied by another matrix, equals that same matrix. 1 0 0 0 1 0 0 0 1 1 0 0 1 Identity Matrices If 𝐴= 𝑎 𝑏 𝑐 𝑑 , then 𝐼= 1 0 0 1 such that 𝑎 𝑏 𝑐 𝑑 ∙ 1 0 0 1 = 1 0 0 1 ∙ 𝑎 𝑏 𝑐 𝑑 = 𝑎 𝑏 𝑐 𝑑

Two 𝑛 𝑥 𝑛 matrices are INVERSES of each other if their product is the identity matrix. Symbols: Inverse of Matrix A: Inverse Matrices

Verify Inverse Matrices – Example #1 Determine whether each pair of matrices are inverses of each other. a. 𝑋= 3 −2 −1 1 and Y= 1 2 1 3 Verify Inverse Matrices – Example #1 b. P= 3 −1 4 −2 and Q= 1 −3 2 4

Verify Inverse Matrices – Guided Practice Determine whether each pair of matrices are inverses of each other. c. M= 4 −1 2 −2 and N= 1 3 − 1 6 1 3 − 2 3 Verify Inverse Matrices – Guided Practice Self-Evaluation - Rate each learning target: Determine whether two matrices are inverses 4 3 2 1 0

Finding Inverse Matrices You can determine whether a matrix has an inverse by looking at its determinant. If det A = 0, then the matrix cannot have an inverse. Finding Inverse Matrices The inverse of matrix 𝐴= 𝑎 𝑏 𝑐 𝑑 is:

Find Inverse Matrices – Example #2 Find the inverse of each matrix, if it exists. S= −1 0 8 −2 𝑇= −4 6 −2 3 Find Inverse Matrices – Example #2

Find Inverse Matrices – Guided Practice Find the inverse of each matrix, if it exists. 𝐴= 8 −5 −3 2 𝐵= 4 −8 −1 2 Find Inverse Matrices – Guided Practice Self-Evaluation - Rate each learning target: Find the inverse of a 2 x 2 matrix 4 3 2 1 0

Self-Evaluation - Rate each learning target: Define new vocabulary: identity matrix; inverse 4 3 2 1 0 Determine whether two matrices are inverses Find the inverse of a 2 x 2 matrix

Assignment: A#4.7 Page 213 # 9 – 21 all Chapter 4 Test Tuesday, 12/9