CCGPS Accelerated Pre-Calculus Unit Five Assignment Packet

Transcription

1 Page 1 Name: Block: CCGPS Accelerated Pre-Calculus Unit Five Assignment Packet Note: This packet is to be completed and turned in no later than. Please be sure to write your last name in ink at the top right corner of each page. Your work and answers must be on another sheet of paper, stapled to this assignment. Each section must be clearly labeled. Students may not work on this packet during instructional time. The answers to the problems can be found in the back of this packet. Students must show work to receive credit for each problem. Mr. Keiger will check on occasion to make sure you are completing the packet. Please ask for help if you need it. Section One: Introduction to Matrices Directions: Use the following matrices to answer the problems one through twelve. 1. State the dimensions of matrix 2. List two matrices that have the same dimensions as matrix 3. State the dimensions of matrix D. 4. State the dimensions of matrix E. 5. State 6. State 7. State 8. State 9. State 10. State 11. State 12. State 13. Give an example of a row matrix. 14. Give an example of a column matrix.

2 Page 2 Section Two: Basic Operation with Matrices Directions: Use the following matrices to answer the problems one through eight. 1. Calculate 2. Calculate 3. Calculate 4. Calculate 2C+A 5. Calculate 2D 6. Calculate 3B+A 7. Calculate A-B 8. Calculate 3E 9. Calculate ( ) 10. Find values for and that make the following equation true. 11. Fill in the matrix to make the following equation true. 12. Fill in the matrix to make the following equation true. 13. Find values for and that make the following equation true. 14. Fill in the matrix to make the following equation true.

3 Page 3 Section Three: Matrix Multiplication 1. Calculate: 2. Calculate: 3. Calculate: 4. Calculate: 5. Multiplication between two real numbers is commutative. This makes. Do you think that multiplication between two matrices is commutative? Consider your answers to problems three and four when answer this question. Section Four: Determinants 1. Calculate the determinant of 2. Calculate the determinant of 3. Calculate the determinant of 4. Calculate the determinant of 5. Calculate: 6. Calculate: 7. Calculate: 8. Calculate: 9. Write two matrices that have the same determinant. 10. Write a matrix with a determinant of zero. Section Five: Mid Unit Review 1. Calculate 3. State the dimensions of 2. Calculate 4. Calculate

4 Page 4 Section Six: Inverse Matrices 1. Find the inverse of 2. Find the inverse of 3. Find the inverse of 4. Find the inverse of 5. Calculate: 6. Calculate: 7. Calculate: 8. Calculate: Section Seven: Solving Systems of Equations Directions: Solve each of the following systems of equations using inverse matrices. 1. { 2. { 3. { 4. { 5. { 6. { Use the following checklist to help you: Represent the system of equations using matrices (coefficient matrix, variable matrix, answer matrix) Find the inverse of the coefficient matrix Multiply both sides of the equation by the inverse of the coefficient matrix

5 Page 5 Section Eight: Using Systems of Equations to Solve Word Problems Directions: Solve the following problems by setting up a system of equations to represent the problem, representing the system using a matrix equation, and solving the problems using inverse matrices. Show your work and write you answer in a complete sentence in terms of the problem. 1. Ronald sells hamburgers for $3.00 each and hot dogs for $1.50 each. If he makes a total of $13.50 selling 7 items, how many of each item does he sell? 2. Sally is selling pencils and erasers. She sells pencils for $3.50 and erasers for $2.00. If she earns $23.50 selling 8 items, how many of each item does she sell? Use the following checklist to help you complete each problem: Set up a system of equations to represent the problem Represent the system of equations using matrices Solve the system of equations using inverse matrices Write the answer in a complete sentence in terms of the problem 1. Define and give an example of a matrix. 2. Define and give an example of a row matrix. Section Nine: Miscellaneous Vocabulary 3. Define and give an example of a column matrix. 4. Explain the difference between multiplying a matrix by a scalar and multiplying a matrix by another matrix. Then, give an example of process. 5. Explain the relationship the identity matrix has with the number one. 6. Draw a vertex edge graph and label the vertices and the edges. 7. State whether the sentence below is true or false. If it is false, give an example that shows that the sentence is false. Matrix addition is commutative. 8. State whether the sentence below is true or false. If it is false, give an example that shows that the sentence is false. Matrix multiplication is commutative.

6 Page 6 Review Section Directions: Use the following matrices to answer questions one (1) through nine (9). 1. Calculate 2. Calculate 3. Calculate 4. Calculate 5. Calculate 6. Calculate 6. Calculate 7. Calculate 8. Calculate 9. Calculate Directions: To solve problems ten and eleven, set up a system of equations to represent the problem, represent the system using a matrix equation, and solve the problems using inverse matrices. Show your work and write you answer in a complete sentence in terms of the problem. 10. A movie theater sells $10.00 tickets to children and $11.50 tickets to adults. If the theater makes $76 selling 7 tickets, how many of each type of ticket does the theater sell? 11. John sells basketball and football cards. He sells basketball cards for $5.00 and football cards $3.50. If he earns $ selling 106 cards, how many of each type of card does he sell? After solving each problem, check back to be sure that you: Set up a system of equations to represent the problem Represented the system of equations using matrices Solved the system of equations using inverse matrices Wrote the answer in a complete sentence in terms of the problem

7 Page 7 Directions: The vertex edge graph below represents available flights on a certain day between Birmingham, Montgomery, Charlotte, Atlanta, Orlando, and Tampa. Use this vertex edge graph to answer problems thirteen through sixteen. 13. List three pairs of cities that have direct flights between them. 14. List three pairs of cities that have no direct flights between them. 15. Samantha wishes to travel from Orlando to Tampa. State two routes she can take. 16. Suppose the flight between Birmingham and Montgomery is cancelled due to inclement weather. Would this affect a traveler trying to fly from Montgomery to Orlando? Why or why not?

8 Page 8 Directions: Suppose the following chart represents the cities that are to be connected with a brand new transportation system in Use this chart to answer problems seventeen through twenty-one. City One Burlington Burlington Concord Springfield Bratlesboro Concord City Two Augusta Concord Manchester Burlington Burlington Bratlesboro 17. Draw a vertex edge graph representing the cities and their connections. 18. Create a matrix to represent to represent the vertex edge graph. 29. Each connection costs forty-five million dollars to construct. Calculate the total cost of construction. 20. Suppose an Ikea builds a distribution center in Augusta and has stores in Manchester and Concord. They are willing to donate forty-five million dollars to the construction of the transportation system if they can have direct paths from Augusta to Manchester and Concord. This means an extra route can be added, but one will have to be taken away. Suggest the route that you would remove and explain your decision. 21. Draw a vertex edge graph representing this new system. Answers: Section One: 1. 2X2 2. A, C 3. 2X3 4. 3X Many correct answers 14. Many correct answers Section Two: Section Three: See solution guide 12. See solution guide See solution guide No

9 Section Four: CCGPS Accelerated Pre-Calculus Assignment Packet Page Many correct answers Section Five: 10. Many correct answers X2 4. Section Six: Section Seven: (2, 3) 2. (1, 2) 3. (2, 3) 4. (-2, 5) 5. (2, 4) 6. (2.5, 3) Section Eight 1. Ronald sells two hamburgers and five hot dogs. 2. Sally sells five pencils and three erasers. Section Nine 1. A matrix is a rectangular array of numbers. (many correct 2. A row matrix is a matrix that consists of one row. (many examples) correct examples) 3. A column matrix is a matrix that consists of one column. 4. Scalar multiplication is multiplying a single number by a (many correct examples) matrix. Matrix multiplication is multiply a matrix by another matrix. (many correct examples) 5. When a matrix is multiplied by the identity matrix, the product 6. See solution guide is the original matrix. 7. True 8. False, see solution guide for explanation *Answers to review section not given. See Mr. Keiger for help. *Please note: solutions to all of these problems can be found on Mr. Keiger s website,