1 / 38

Splash Screen

Splash Screen. Lesson 4-1 Introduction to Matrices Lesson 4-2 Operations with Matrices Lesson 4-3 Multiplying Matrices Lesson 4-4 Transformations with Matrices Lesson 4-5 Determinants Lesson 4-6 Cramer's Rule Lesson 4-7 Identity and Inverse Matrices

igor-morin
Download Presentation

Splash Screen

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Splash Screen

  2. Lesson 4-1Introduction to Matrices Lesson 4-2 Operations with Matrices Lesson 4-3 Multiplying Matrices Lesson 4-4 Transformations with Matrices Lesson 4-5 Determinants Lesson 4-6 Cramer's Rule Lesson 4-7 Identity and Inverse Matrices Lesson 4-8 Using Matrices to Solve Systems of Equations Chapter Menu

  3. Five-Minute Check (over Chapter 3) Main Ideas and Vocabulary Example 1: Real-World Example: Organize Data intoa Matrix Example 2: Dimensions of a Matrix Example 3: Solve an Equation Involving Matrices Lesson 1 Menu

  4. Organize data in matrices. • Solve equations involving matrices. • matrix • equal matrices • element • dimension • row matrix • column matrix • square matrix • zero matrix Lesson 1 MI/Vocab

  5. Organize Data into a Matrix COLLEGEKaitlin wants to attend one of three Iowauniversities next year. She has gathered information about tuition (T), room and board (R/B), and enrollment (E) for the universities. Use a matrix to organize the information. Which university’s total cost is lowest? Iowa State University: T - $5426 R/B - $5958 E - 26,380 University of Iowa: T - $5612 R/B - $6560 E - 28,442 University of Northern Iowa: T - $5387 R/B - $5261 E - 12,927 Lesson 1 Ex1

  6. T R/B E ISU UI UNI Organize Data into a Matrix Organize the data into labeled columns and rows. Answer: The University of Northern Iowa has the lowest total cost. Lesson 1 Ex1

  7. DINING OUT Justin is going out for lunch. The information he has gathered from two fast-food restaurants is listed below. Use a matrix to organize the information. When is each restaurant’s total cost less expensive? Lesson 1 CYP1

  8. A. The Burger Complex has the best price for chicken sandwiches. The Lunch Express has the best prices for hamburgers and cheeseburgers. B. The Burger Complex has the best price for hamburgers and cheeseburgers. The Lunch Express has the best price for chicken sandwiches. C. The Burger Complex has the best price for chicken sandwiches and hamburgers. The Lunch Express has the best prices for cheeseburgers. D. The Burger Complex has the best price for cheeseburgers. The Lunch Express has the best price for chicken sandwiches and hamburgers. • A • B • C • D Lesson 1 CYP1

  9. State the dimensions of matrix G if 2 rows 4 columns Dimensions of a Matrix Answer: Since matrix G has 2 rows and 4 columns, the dimensions of matrix G are 2 × 4. Lesson 1 Ex2

  10. State the dimensions of matrix G if G = • A • B • C • D A. 2 × 3 B. 2 × 2 C. 3 × 2 D. 3 × 3 Lesson 1 CYP2

  11. Solve an Equation Involving Matrices Since the matrices are equal, the corresponding elements are equal. When you write the sentences to solve this equation, two linear equations are formed. y = 3x – 2 3 = 2y + x Lesson 1 Ex3

  12. Solve an Equation Involving Matrices This system can be solved using substitution. 3 = 2y + x Second equation 3 = 2(3x – 2) + x Substitute 3x – 2 for y. 3 = 6x – 4 + x Distributive Property 7 = 7x Add 4 to each side. 1 = x Divide each side by 7. Lesson 1 Ex3

  13. Solve an Equation Involving Matrices To find the value for y, substitute 1 for x in either equation. y = 3x – 2 First equation y = 3(1) – 2 Substitute 1 for x. y = 1 Simplify. Answer: The solution is (1, 1). Lesson 1 Ex3

  14. A • B • C • D A. (2, 5) B. (5, 2) C. (2, 2) D. (5, 5) Lesson 1 CYP3

  15. End of Lesson 1

  16. Five-Minute Check (over Lesson 4-1) Main Ideas and Vocabulary Key Concept: Addition and Subtraction of Matrices Example 1: Add Matrices Example 2: Subtract Matrices Example 3: Real-World Example Key Concept: Scalar Multiplication Example 4: Multiply a Matrix by a Scalar Concept Summary: Properties of Matrix Operations Example 5: Combination of Matrix Operations Lesson 2 Menu

  17. Add and subtract matrices. • Multiply by a matrix scalar. • scalar • scalar multiplication Lesson 2 MI/Vocab

  18. Lesson 2 KC1

  19. Answer: Add Matrices Definition of matrix addition Add corresponding elements. Simplify. Lesson 2 Ex1

  20. Add Matrices Answer: Since the dimensions of A are 2 × 3 and the dimensions of B are 2 × 2, these matrices cannot be added. Lesson 2 Ex1

  21. A. B. C. D. • A • B • C • D Lesson 2 CYP1

  22. A. B. C. D. • A • B • C • D Lesson 2 CYP1

  23. Answer: Subtract Matrices Definition of matrix subtraction Subtract corresponding elements. Simplify. Lesson 2 Ex2

  24. A. B. C. D. • A • B • C • D Lesson 2 CYP2

  25. SCHOOL ATHLETESThe table below shows the total number of student athletes and the number of female athletes in three high schools. Use matrices to find the number of male athletes in each school. Lesson 2 Ex3

  26. total female male The data in the table can be organized into two matrices. Find the difference of the matrix that represents the total number of athletes and the matrix that represents the number of female athletes. Subtract corresponding elements. Lesson 2 Ex3

  27. Answer: There are 582 male athletes at Jefferson, 286 male athletes at South, and 677 male athletes at Ferguson. Lesson 2 Ex3

  28. TESTS The table below shows the percentage of students at Clark High School who passed the 9th and 10th grade proficiency tests in 2001 and 2002. Use matrices to find how the percentage of passing students changed from 2001 to 2002. Lesson 2 CYP3

  29. A. B. C.D. 9th grade 9th grade 9th grade 9th grade 10th grade 10th grade 10th grade 10th grade Math Reading Science Citizenship Math Reading Science Citizenship Math Reading Science Citizenship Math Reading Science Citizenship • A • B • C • D Lesson 2 CYP3

  30. Lesson 2 KC2

  31. Multiply a Matrix by a Scalar Substitution Lesson 2 Ex4

  32. Multiply a Matrix by a Scalar Multiply each element by 2. Simplify. Answer: Lesson 2 Ex4

  33. A.B. C.D. • A • B • C • D Lesson 2 CYP4

  34. Lesson 2 CS1

  35. 4A – 3B Combination of Matrix Operations Perform the scalar multiplication first. Then subtract the matrices. Substitution Multiply each element in the first matrix by 4 and each element in the second matrix by 3. Lesson 2 Ex5

  36. Combination of Matrix Operations Simplify. Subtract corresponding elements. Simplify. Answer: Lesson 2 Ex5

  37. A. B. C. D. • A • B • C • D Lesson 2 CYP5

  38. End of Lesson 2

More Related