Find the following matrix products, if possible.(1-4)

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1 Name: Math 1324 Activity 8(4.5)(Due by Oct. 13) Dear Instructor or Tutor, These problems are designed to let my students show me what they have learned and what they are capable of doing on their own. Please allow them to work the problems on their own! If you would like to help them with similar problems, here are the related homework problems: pg. 231:19-67 odd, 73, 75. Thanks! Dear Student, Don t even think about asking for help on the problems in this activity! The recommended homework problems have answers in the book, so do them first for practice!!! Find the following matrix products, if possible.(1-4) Determine if the given pairs of matrices are inverses. Show work.(5-6) ,

2 , Find the inverse, if it exists, for the following matrices. Show work. (7-10)

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4 11. Burger Barn s three locations sell hamburgers, fries, and soft drinks. Barn I sells 900 burgers, 600 orders of fries, and 750 soft drinks each day. Barn II sells 1500 burgers, 950 orders of fries, and 900 soft drinks each day. Barn III sells 1150 burgers, 800 orders of fries, and 825 soft drinks each day. a) Complete the 3 3 matrix, S, that represents the sales figures for all three locations. Barn I Barn II Barn III 900 S Burger Fries Soft Drink b) Burgers cost $2.00 each, fries $1.50 an order, and soft drinks $1.00 each. Complete the 1 3 matrix P that displays the prices. Burger Fries Drink P c) What matrix product displays the daily revenue at each of the three locations? d) Compute this matrix product to determine the daily revenue at each location.

5 12. A nationwide air freight service has connecting flights between five cities as illustrated in the diagram. To represent this schedule in matrix form, we construct a 5 5 incidence matrix A, where the row numbers represent the origin of each flight and the column numbers represent the destinations. We place a 1 in the i th row and j th column of this matrix if there is a connecting flight from the i th city to the j th city; otherwise, insert a 0. We also place zeros on the diagonal because a connecting flight with the same origin and destination makes no sense. With the schedule represented in this matrix form, we can perform operations on this matrix to obtain information about the schedule. Atlanta Baltimore Chicago a) Complete the 5 5 incidence matrix A. b) Find 2 A. Origin Destination Denver El Paso A

6 2 c) What does the 1 in Row 2 and Column 1 of A indicate about the schedule? What does the 2 in Row 1 and Column 3 indicate about the schedule? In general, how would you 2 interpret each element not on the diagonal of A? d) Find 3 A. 3 e) What does the 1 in Row 4 and Column 2 of A indicate about the schedule? What does the 2 in Row 1 and Column 5 indicate about the schedule? In general, how would you 3 interpret each element not on the diagonal of A? f) Compute A, A A, A A A, until you obtain a matrix with no 0 entries(except possibly on the diagonal), and interpret.

7 Bonus#1: A famous problem has a shepherd, a boat, a wolf, a sheep, and a cabbage on the left side of a river. The shepherd is to transport everything - himself, the boat, the animals, and the cabbage - to the right side of the river. He cannot leave the wolf and the sheep or the sheep and the cabbage unattended, and he can carry at most one occupant(in addition to himself) in the boat at one time. The states in this problem will be the list of inhabitants on the left bank of the river. The only allowable states are then S 1 = [boat, shepherd, wolf, sheep, cabbage], S 2 = [boat, shepherd, wolf, sheep], S 3 = [boat, shepherd, wolf, cabbage], S 4 = [boat, shepherd, sheep, cabbage], S 5 = [boat, shepherd, sheep], S 6 = [], S 7 = [cabbage], S 8 = [sheep], S 9 = [wolf], S 10 = [wolf, cabbage]. Here is the 10 x 10 incidence matrix, A: End of boat trip S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S S S S Start of boat trip S = A S S S S S Determine the fewest number of crossings in which the deed can be done - if, indeed, it can be done, by considering powers of the incidence matrix A. The deed is done if there is at least one route from S 1 to S 6. Bonus#2: Given the following incomplete distance chart for 4 points in a plane, find the distance from A to B. A B C D A 0? 21 9 B? C D

8 Bonus#3: dimension dimensions are multiplied. Bonus: Decode the contents of the rectangle into a familiar word or phrase. come serve come serve come serve come serve