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# Inverses of Matrices

Lesson 5 of 12

## Objective: SWBAT find the inverse of a 2 x 2 matrix.

## Big Idea: Students discover how to find the inverse of a matrix by analyzing the relationships between matrices and their inverses.

*50 minutes*

#### Warmup

*7 min*

Today, I start class by giving students five minutes to complete the first two sections of the Mystical Matrices Worksheet. As they work, I say, "Pay particular attention to the arithmetic and the commonalities of each exercise." With about a minute remaining, I will ask students to use their graphing calculators to quickly multiply the last few matrices. I want them to do at least one by hand, but for this lesson the calculator will allow students to complete more examples and thereby have more results for comparison when we discuss.

Once time is up, we will work as a class to complete the missing information in the third section of the Worksheet. As we discuss their work, it is important for students to recognize the role of the zero and of the identity matrix in addition and subtraction of matrices.

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#### Closure

*3 min*

To close today's lessons on a positive note, I will ask my students to reflect on today’s learning by discussing the **3 W's Closure**** **in their teams. I introduce the 3 W's on page 2 of Flipchart-Inverses of Matrices.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Basic Matrix Operations
- LESSON 2: Matrices in the World Around Us
- LESSON 3: Determinants and Area of a Triangle (Day 1 of 2)
- LESSON 4: Determinants and Area of a Triangle (Day 2 of 2)
- LESSON 5: Inverses of Matrices
- LESSON 6: Applications of Inverses - Decoding
- LESSON 7: Solving Systems of Equations using Inverse Matrix Operations
- LESSON 8: Cramers Rule - Solving Systems of Equations
- LESSON 9: Determining the Matrix for Transformations
- LESSON 10: Matrix Transformations
- LESSON 11: Matrices Test Review
- LESSON 12: Matrices Exam