# Mathematics

## Instructions

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

There are 150 examination points on this EX2, worth 15 CPs. Make sure to appropriately rename the workbook by replacing Name in the filename with your last name plus immediate first initial, and change nothing else (as we have been doing). However, if you do not appropriately rename the file, you will automatically lose 15% of your points. Hence, it is in your best interests to let me look at your file before you submit it if you have any questions, including the filename. Make sure to also follow my formatting instructions. As stated in the GEN101 activities and documents: If you correctly format the cells but have a wrong answer, some partial credit is likely, but If you incorrectly format the cells, then it won’t matter whether you performed the calculations correctly: It’s wrong! Again, feel free to email should you have any questions; please remember to identify your course in the email subject line, and to also attach a current copy of your examination. Make sure to NOT type in any values where calculations are required, which is just about everywhere. I will let you know when you may type in a value, if applicable. IF you type a value directly into any cell not authorized by me, then you will lose ALL points for that worksheet Again, if you are unsure about this or anything else anywhere in the examination, email me.

## 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