1. Today, you will be able to:
Algebra Wednesday
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

2. 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

3. Intro to Inverse Matrices

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

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

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

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

8. 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:

9. 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

10. 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

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

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