1. My Math 3 website is martinmathsite.wikispaces.com You will find my PowerPoint (without some of the answers) and most of the worksheets or assignments there.

2. Essential Question: How do we use matrices to solve problems? How do we apply operations to matrices? Standards: MM3A4: Students will perform basic operations with matrices MM3A4a: Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

3. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1.a) Who does student A consider a friend and yet does not trust enough to loan $10. Core-plus 2 p. 83

4. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1.a) Who does student A consider a friend and yet does not trust enough to loan $10. (Students b and C are people who student A considers friends but does not trust enough to loan $10.) Core-plus 2 p. 83

5. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1. a)Who does student A consider a friend and yet does not trust enough to loan $10. b)Do you think it is reasonable that a student could have a friend who he or she does not trust enough to loan $10. Core-plus 2 p. 83

6. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1. a)Who does student A consider a friend and yet does not trust enough to loan $10. b)Do you think it is reasonable that a student could have a friend who he or she does not trust enough to loan $10. c)Who does student B trust and yet does not consider a person to be friends? Core-plus 2 p. 83

7. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1. a)Who does student A consider a friend and yet does not trust enough to loan $10. b)Do you think it is reasonable that a student could have a friend who he or she does not trust enough to loan $10. c)Who does student B trust and yet does not consider a person to be friends? (Student B trusts student A, yet does not consider A to be a friend.) Core-plus 2 p. 83

8. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1.a) Who does student A consider a friend and yet does not trust enough to loan $10. b) Do you think it is reasonable that a student could have a friend who he or she does not trust enough to loan $10. c) Who does student B trust and yet does not consider a person to be friends d) Who does student D trust and also consider to be a friend? Core-plus 2 p. 83

9. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1.a) Who does student A consider a friend and yet does not trust enough to loan $10. b) Do you think it is reasonable that a student could have a friend who he or she does not trust enough to loan $10. c) Who does student B trust and yet does not consider a person to be friends d) Who does student D trust and also consider to be a friend? (Student D trust students B and E and considers them to be friends.) Core-plus 2 p. 83

10. Investigation 3: Combining Matrices You can analyze these matrices together to see how friendship and trust are related in this group of five students. Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0 1.a) Who does student A consider a friend and yet does not trust enough to loan $10. b) Do you think it is reasonable that a student could have a friend who he or she does not trust enough to loan $10. c) Who does student B trust and yet does not consider a person to be friends d) Who does student D trust and also consider to be a friend? 2.A friend you trust is a trustworthy friend. a) Combine the movie and loan matrices to construct a new matrix that shows who each of the five students considers to be a trustworthy friend. Core-plus 2 p. 83

11. Let’s work this one together. 2.A friend you trust is a trustworthy friend. a) Combine the movie and loan matrices to construct a new matrix that shows who each of the five students considers to be a trustworthy friend. A B C D E A B C D E Core-plus 2 p. 83 Movie Matrix Loan Matrix with to A B C D E A B C D E A 0 1 1 1 1 A 0 0 0 1 1 B 0 0 1 1 1 B 1 0 0 1 0 Would Like to C 1 0 0 1 0 Would Loan C 0 0 0 1 0 Go to a Movie D 0 1 1 0 1 Money D 1 1 0 0 1 E 1 0 0 1 0 E 0 1 1 0 0

12. 3.a. Construct a matrix G with dimensions [1 x 3] corresponding to production cost per item. b. Use this new matrix G and matrix E from #1 to find matrix P, the profit the Booster Club can expect from the sale of each bear, tote bag, and tee shirt. Another type of matrix operation is known as scalar multiplication. A scalar is a single number such as 3 and matrix scalar multiplication is done by multiplying each entry in a matrix by the same scalar. For example, if, then. Booster Club Learning Task Extension:

13. Complete worksheet “Adding and Subtracting Matrices” with a partner. Put your name at the top of the page and your partner’s name at the bottom of the page.

14. 6.Consider the following matrices. 2 -4 6 2 3 -6 A = 0 1.5 3 B = 0 1 6.5 7 -3.5 8 11 -3 6 1 -1 6 1 0 -1 1.25 0 C = 0 1 D = 8 -12 5 1 1 0 0 18 a. Compute B + D. b. Compute 6C. c. Compute –A. d. Compute B + B e. Compute 2B + 3D. f. Compute D – B. g. Compute a new matrix E that could be added to A. Then compute A + E. 16. For any matrix A, can you always compute A + A? Why or why not? Core-Plus 2 p. 91 Core-Plus 2 p. 96

15. Math 3 Preview and Acceleration Unit 1, Lesson 1, Day 2 (Previewing Day 3) These Matrix Multiplication Problems Are Possible 1362 4 45-1 ∙3-2 1 5 5-3 8 ∙ 3 -2 -1 2 4 6 1 5 9 4 ∙ 1 3 8 9 5 9 1 2 3 4 5 6 7 8 910 1112 13. 14 15 16 17 18 19 20 21 22 23 24 25 -8 -7-4 -510 2 1 5 -3 -2. 1 8 -3 10-4 1 7 3 9 4

16. These Matrix Multiplication Problems Are Not Possible 136.241 45-13-23 5-3 8 ∙ 3 -2 -1 2 4 6 413 5 ∙48 992 1 2 3 4 5 6 7 9 10 11 12 13. 14 15 17 18 20 21 -8 -7 -4 -5102 1 5 -3 -2. 1 8 -3 10 -4 1