1. We are Playing Attack
The castle you just drew on the board is under attack.
I will give you a question. You will need to work together in groups to answer the question. Everyone must have the work/answer on their paper.
I will randomly select one group and one person in that group to answer the question (work and answer must be shown).
If they get it right, then they get to choose different castles to “attack” (put an x on them). The number of attacks is based on how long you have to solve the question. One of your attacks can be defense to build back your castle.
If they get it wrong, then I attack their castle.
When you have three x’s, your castle is gone.
Last castle standing wins three bonus points on their test.

2. What is the size of A? What is the size of B?

3. How many elements are in b?

4. What is the value of C12? C21?

5. What is A + C?

6. What is C – B?

7. What is 2A + D?

8. The dimensions of matrices P, Q, R, and S are 3x2, 3x3, 4x3, and 2x3, respectively. If matrix multiplication is possible, find the dimensions of the following matrix products. If it is not possible, state why. QP RQ QS
RPS

9. Find AB.

10. Find BA.

11. Find CA.

12. Find DA + E.

13. Three music classes at Central High are selling candy as a fundraiser
Three music classes at Central High are selling candy as a fundraiser. The number of each kind of candy sold by each of the three classes is shown in the following table:
Jazz Band
Symphonic Band
Orchestra
Almond Bars
300
220
250
Chocolate Chews
240
330
400
Mint Patties
150
200
180
Sour Gummies
175
160
The profit for each type of candy is sour gummies, 30 cents; chocolate chews, 50 cents, almond bars, 25 cents; and mint patties, 35 cents. Use matrix multiplication to compute the profit made by each class on its candy sales.

14. Which of the following matrices are inverses of each other? Explain

15. The students at central high are planning to hire a band for the prom
The students at central high are planning to hire a band for the prom. Their choices are bands a, b, and c. They survey the 10th, 11th, and 12th grade classes and find the following percentage of students prefer the bands:
The student population by class and gender is:
Use matrix multiplication to find:
The number of males and females who prefer each band.
The total number of students who prefer each band.

16. The characteristics of the female population of a herd of small mammals are shown in the following table:
0-4
4-8
8-12
12-16
16-20
20-25
Birth rates
0.5
1.1
0.9
0.4
Survival rates
0.6
0.8
Suppose the initial female population for the herd is given by:
What is the life expectancy of this mammal?
Construct the Leslie matrix for this application.
How many mammals will there be in each age group after six cycles?
How many mammals will there be in TOTAL after 6 cycles?

17. Solve for x and y.

18. Solve for Matrix X.

19. Solve for matrix X.

20. Find the inverse:

21. Mike and Brit are playing poker for pennies
Mike and Brit are playing poker for pennies. Mike is holding a very poor hand and is considering bluffing or not bluffing. Brit can either call or not call the bluff. The payoff matrix for the situation is below. What is each person’s best strategy? Is this a strictly determined game? If so, what is the saddle point?

22. Suppose that in the final days of a political campaign for mayor, the democrats and republicans are planning their strategies for winning undecided voters to their political camps. The democrats have decided on two strategies, plan A and plan B. The republicans plan to counter with plans C and D. The following matrix gives the payoff for the democrats of the various combinations of strategies. The numbers represent the percentage of the undecided voters joining the democrats in each case. What is each person’s best strategy? Is this a strictly determined game? If so, what is the saddle point?

23. Depending on their driving records, Charlotte drivers are classified in one of the following categories: 1. Elite, 2. Good, 3. Regular, and 4. Poor. Each driver’s category varies from year to year according to a Markov model whose transition matrix is:
Find the probability that an initially Good driver becomes a Poor driver in 4 years.
Find the probability that an initially Poor driver becomes an Elite driver in 8 years.

24. A large group of mice is kept in a cage having connected compartments A, B, and C. Mice in Compartment A move to B with probability 0.3 and to C with probability Mice in B move to A or C with probabilities 0.15 and 0.55, respectively. Mice in C move to A and B with probabilities 0.3 and 0.6 respectively:
Construct a transition matrix to represent this situation. Hint: You will have to also find the probability that the mice do NOT move.
If your favorite mouse starts out in compartment C, find the probability that he will be in A after 7 transitions.

25. Code the message “I love discrete math” using the coding matrix:

26. Decode the following message if the initial coding matrix was:
Initial message: