1. Today: Return C3 Test Goal Evaluation 4.1 Matrices Calculator Activity Finish 4.1 Instruction Practice Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence. Helen Keller Integrated

2. Objectives: 1.Identify the characteristics of a matrix. 2.Add and subtract matrices. 3.Solve matrix equations. 4.Use matrices in a real life example. Vocabulary: row, column, row matrix, column matrix, square matrix, zero matrix, scalar, matrix equation Matrix Operations 4.1

3. Matrix Operations 4.1 A is a 2x3 matrix. Anatomy of a Matrix (Matrices) Identify this matrix: 2 x 3

4. Matrix Operations 4.1 A is a 2x3 matrix. Identify this matrix: Anatomy of a Matrix (Matrices) 3 x 5

5. Matrix Operations 4.1 A is a 2x3 matrix. Identify this matrix: Anatomy of a Matrix (Matrices) 4 x 3

6. Matrix Operations 4.1 A is a 2x3 matrix. Identify this matrix: Anatomy of a Matrix (Matrices) column matrix 3 x 1

7. Matrix Operations 4.1 A is a 2x3 matrix. Identify this matrix: Anatomy of a Matrix (Matrices) row matrix1 x 4

8. Matrix Operations 4.1 A is a 2x3 matrix. Identify this matrix: Anatomy of a Matrix (Matrices) square matrix 3 x 3

9. Matrix Operations 4.1 A is a 2x3 matrix. Identify this matrix: Anatomy of a Matrix (Matrices) zero matrix 3 x 2

10. Write a matrix to organize the following information about school lunch menus. High School: 5 entrees, 3 desserts, 5 drinks Middle School: 3 entrees, 2 desserts, 4 drinks Example 1 Writing a Matrix

11. Matrix Operations 4.1 Each entry has its own address. (row, column)

12. Matrix Operations 4.1 Each entry has its own address. (row, column) 1,1 2,12,2 1,21,3 2,3

13. Matrices are equal if they are the same size and each entry is equal. If A = J, then find the value of the variables. Example 2 Find for Variables in a Matrix

14. Matrices are equal if they are the same size and each entry is equal. If A = K, then find the value of the variables. Example 2 Find for Variables in a Matrix

15. Matrix Operations 4.1 Calculator Activity

16. To add or subtract matrices: 1.matrices same size 2.add/subtract same entries Find:L + M Example 3 Adding and Subtracting Matrices

17. To add or subtract matrices: 1.matrices same size 2.add/subtract same entries Find:M + N Example 3 Adding and Subtracting Matrices Can’t be done.

18. To add or subtract matrices: 1.matrices same size 2.add/subtract same entries Find:N + R Example 3 Adding and Subtracting Matrices Can’t be done.

19. To add or subtract matrices: 1.matrices same size 2.add/subtract same entries Find:M – R Example 3 Adding and Subtracting Matrices

20. To add or subtract matrices: 1.matrices same size 2.add/subtract same entries Find:P – L Example 3 Adding and Subtracting Matrices Can’t be done.

21. To add or subtract matrices: 1.matrices same size 2.add/subtract same entries Find:Q – N Example 3 Adding and Subtracting Matrices

22. Congress: The United States Congress is composed of the House of Representatives and the Senate. The matrices below show the number of men and women in the Senate and House in 1999 for 106 th Congress. Write and label a single matrix that show the number of men and women in Congress Example 4 Real World: US Congress HouseSenate

23. Profit: You own two stores that sell household appliances. The matrices below show revenue and expenses for three months at each store Example 4 Real World: Profit Matrix Revenue $ Expenses $ Profit $

24. To multiply a scalar: 1.Multiply the scalar with every entry Perform the scalar multiplication: Example 5 Multiply a Matrix by a Scalar

25. To solve a matrix equation: 1.Simplify both sides of the equation. 2.Set up equations and solve 3.Present answers 4.Check Solve: x = 6, y = -2 Example 6 Solve a Matrix Equation

26. To solve a matrix equation: 1.Simplify both sides of the equation. 2.Set up equations and solve 3.Present answers 4.Check Solve: x = 10, y = 2 Example 6 Solve a Matrix Equation

27. Assignment: 4.1 p89 #7-25, 27, 28 Progress Report Signature Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence. Helen Keller Integrated