# Mathematics

## Instructions

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

## EX2-1 50

 Set up and solve each of the following as directed; points as defined (50 points total on this WS). #1-1 a b c d [C] [V] [R] You may type in these rows ¯ ¯ ¯ a = Þ b c d [C]-1 [V] [C]-1[R] Initial Solution ¯ (10 pts) Set up the above system and solve as indicated. a = ¬ Type in your initial solution’s VALUES here (Cells M11-14) b c d 5 points #1-2 ¯ (10 pts) Express the values in [C] in fractional form up to 3 digits [C] [V] [R] x1 = ¬ Type in values along these rows Þ x2 x3 5 ­ points Careful! Watch your formats!! [C]-1 [V] [C]-1[R] x1 = ¬ Express your solutions as fractions up to 3 digits x2 x3 10 ­ points 5 ­ points

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

Type in your initial solution where indicated along Column M . (5 pts) Then change element r21 at the left to a value of 4 >> SAVE!

## EX2-2 50

 Set up and run your matrices below the diagram; report the steady state matrix to 4 decimal places Remember to be VERIDICAL 25 points for the One-Step transition matrix being set up correctly 15 points for your remaining matrices up to the steady state matrix You MUST calculate in Excel the values along the main diagonal (Customer Loyalty) by utilizing the values along Column S. SRow ¯ A B C D A 1 B 1 ¬ Watch format of One-Step Matrix’s values! C 1 Be VERIDICAL !!! D 1 See text box for instructions for values along Main Diagonal These values MUST be calculated IN EXCEL Using the respective values along Column S!!

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

The diagram at the right represents what proportion of a company’s customers each fiscal quarter transition to another company for its products and services. Obviously, some customers stay with each company, these are denoted by the shaded cells along the One-Step Transition Matrix’s main diagonal. Any proportions remaining coming out of each company are customers that stay with that company. You MUST calculate each company’s customer loyalty % by selecting the values along Column S. Set up the One-Step transition matrix based on the graphic and the instructions immediately above; make sure to finish shading in the matrix’s cells. Then find the steady state matrix, after which you will be able to answer this question: In the long run, which company will most probably maintain the greatest market share? (10 pts) Answer Here 

## EX2-3 50

 Set up and solve each of the following as directed; points as defined (50 points total). #1-3 1.4 2.8 2.3 2.1 2.6 1.8 1.9 [C] [V] [R] Make sure to shade in matrices; not too dark u v w x y z u = v w x y z [C]-1 [V] [C]-1[R] Make sure to shade in matrices; not too dark ROUND FINAL VALUES TO ONE DECIMAL PLACE #1-4 [A] R1 R1[A]-1 1 2 -1 34 83 47 1 A 14 N 2 5 2 2 B 15 O -1 -2 2 3 C 16 P R2 R2[A]-1 4 D 17 Q 32 82 45 5 E 18 R [A]-1 6 F 19 S 7 G 20 T R3 R3[A]-1 8 H 21 U 32 85 66 9 I 22 V 10 J 23 W 11 K 24 X 12 L 25 Y 13 M 26 Z SAVE!!

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

You MUST use the values in these two rows by tying them together in Excel to generate the values in the second row. THE 2nd ROW IS THE ONLY ROW YOU CANNOT JUST TYPE IN!! 30 pts for setting up and solving system; 10 pts for solutions

Using the matrices above and the lexicon at the right, decode the message and type it out below in this text box (10 pts): Message 

0

0

6

8

=

=

+

=

+

+

=

+

+

+

d

a

d

c

b

a

d

c

b

a

d

c

b

a

0

0

6

8









da

dcba

dcba

dcba

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