EBK FINITE MATHEMATICS
7th Edition
ISBN: 8220103611954
Author: Costenoble
Publisher: Cengage Learning US
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Textbook Question
Chapter 6.4, Problem 10E
In Exercises 1–16, evaluate the number. [HINT: See Quick Examples 4–7.]
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
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Chapter 6 Solutions
EBK FINITE MATHEMATICS
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - In Exercises 1720, draw a Venn diagram that...Ch. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - In Exercises 3542, A={small,medium,large},...Ch. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - In Exercises 3542, A={small,medium,large},...Ch. 6.1 - Prob. 41ECh. 6.1 - In Exercises 3542, A={small,medium,large},...Ch. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 6.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.1 - Databases A freelance computer consultant keeps a...Ch. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Databases A freelance computer consultant keeps a...Ch. 6.1 - Databases A freelance computer consultant keeps a...Ch. 6.1 - Prob. 67ECh. 6.1 - Databases A freelance computer consultant keeps a...Ch. 6.1 - Prob. 71ECh. 6.1 - You sell two models of music players: the yoVaina...Ch. 6.1 - Prob. 73ECh. 6.1 - Prob. 74ECh. 6.1 - Prob. 75ECh. 6.1 - Prob. 76ECh. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.1 - Prob. 79ECh. 6.1 - Prob. 80ECh. 6.1 - Prob. 81ECh. 6.1 - Prob. 82ECh. 6.1 - When this book was being written, the copy editor...Ch. 6.1 - When an older version of this book was being...Ch. 6.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 6.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 6.2 - If n(A)=43,n(B)=20, and n(AB)=3, find n(AB).Ch. 6.2 - If n(A)=60, n(B)=20, and n(AB)=1 find n(AB).Ch. 6.2 - If n(AB)=100andn(A)=n(B)=60, fi0nd n(AB).Ch. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - In Exercises 2730, use the given information to...Ch. 6.2 - In Exercises 2730, use the given information to...Ch. 6.2 - Prob. 30ECh. 6.2 - Web Searches In November 2011 a search using the...Ch. 6.2 - Web Searches In November 2011 a search using the...Ch. 6.2 - Amusement On a particularly boring transatlantic...Ch. 6.2 - Restaurant Menus While scanning through the...Ch. 6.2 - Mobile Gamers Of a total of 132 million mobile...Ch. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Housing Starts Exercises 4348 are based on the...Ch. 6.2 - Housing Starts Exercises 4348 are based on the...Ch. 6.2 - Housing Starts Exercises 4348 are based on the...Ch. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Stocks Exercises 4954 are based on the following...Ch. 6.2 - Stocks Exercises 4954 are based on the following...Ch. 6.2 - Stocks Exercises 4954 are based on the following...Ch. 6.2 - Stocks Exercises 4954 are based on the following...Ch. 6.2 - Stocks Exercises 4954 are based on the following...Ch. 6.2 - Medicine In a study of Tibetan children,10 a total...Ch. 6.2 - Prob. 56ECh. 6.2 - Entertainment According to a survey of 100 people...Ch. 6.2 - Athletics Of the 4,700 students at Medium Suburban...Ch. 6.2 - Entertainment In a survey of 100 Enormous State...Ch. 6.2 - Entertainment Refer back to Exercise 59. You are...Ch. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Why is the Cartesian product referred to as a...Ch. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - Prob. 70ECh. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.3 - An experiment requires a choice among three...Ch. 6.3 - Prob. 2ECh. 6.3 - An experiment requires a sequence of three steps....Ch. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - How many different four-letter sequences can be...Ch. 6.3 - How many different five-letter sequences can be...Ch. 6.3 - Ice Cream When Baskin-Robbins was founded in 1945,...Ch. 6.3 - Ice Cream At the beginning of 2002, Baskin-Robbins...Ch. 6.3 - Binary Codes A binary digit, or bit, is either 0...Ch. 6.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 6.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 6.3 - Binary Codes A binary digit, or bit, is either 0...Ch. 6.3 - Reward While selecting candy for students in his...Ch. 6.3 - Productivity Professor Oger must choose between an...Ch. 6.3 - Prob. 23ECh. 6.3 - Radar Detectors Radar detectors are either powered...Ch. 6.3 - Multiple-Choice Tests Professor Easys final...Ch. 6.3 - Multiple-Choice Tests Professor Toughs final...Ch. 6.3 - Tests A test requires that you answer either Part...Ch. 6.3 - Tests A test requires that you answer first Part A...Ch. 6.3 - Stock Portfolios Your broker has suggested that...Ch. 6.3 - Menus The local diner offers a meal combination...Ch. 6.3 - Prob. 31ECh. 6.3 - Computer Codes Some written languages, such as...Ch. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Variables in Visual Basic A variable name in the...Ch. 6.3 - Prob. 36ECh. 6.3 - Tournaments How many ways are there of filling in...Ch. 6.3 - Tournaments How many ways are there of filling in...Ch. 6.3 - Telephone Numbers Suppose a telephone number...Ch. 6.3 - Social Security Numbers A Social Security Number...Ch. 6.3 - Credit Card Numbers The vast majority of Visa and...Ch. 6.3 - Credit Card Numbers Credit cards issued by...Ch. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - HTML Colors in HTML (the language in which many...Ch. 6.3 - Telephone Numbers In the past, a local telephone...Ch. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - Prob. 49ECh. 6.3 - License Plates17 License plates in Montana have a...Ch. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Car Engines Repeat Exercise 53 for an...Ch. 6.3 - Minimalist Art You are exhibiting your collection...Ch. 6.3 - Prob. 56ECh. 6.3 - Product Design Your company has patented an...Ch. 6.3 - Product Design Your company has patented an...Ch. 6.3 - Calendars The World Almanac19 features a perpetual...Ch. 6.3 - Calendars How many possible calendars are there...Ch. 6.3 - Prob. 61ECh. 6.3 - Programming in Java Script (Some programming...Ch. 6.3 - Prob. 63ECh. 6.3 - Prob. 64ECh. 6.3 - Morse Code In Morse code, each letter of the...Ch. 6.3 - Numbers How many odd numbers between 10 and 99...Ch. 6.3 - Prob. 67ECh. 6.3 - Prob. 68ECh. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - Prob. 71ECh. 6.3 - Find an interesting application that requires a...Ch. 6.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 6.4 - Prob. 9ECh. 6.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 6.4 - Prob. 11ECh. 6.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 6.4 - Prob. 16ECh. 6.4 - How many ordered lists are there of four items...Ch. 6.4 - How many ordered sequences are possible that...Ch. 6.4 - Prob. 19ECh. 6.4 - How many unordered sets are there of four items...Ch. 6.4 - Prob. 21ECh. 6.4 - How many six-letter sequences are possible that...Ch. 6.4 - Prob. 23ECh. 6.4 - How many three-letter sequences are possible that...Ch. 6.4 - How many three-letter (unordered) sets are...Ch. 6.4 - How many three-letter (unordered) sets are...Ch. 6.4 - Prob. 27ECh. 6.4 - How many six-letter sequences are possible that...Ch. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Prob. 31ECh. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Prob. 33ECh. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Prob. 36ECh. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Prob. 38ECh. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Marbles For Exercises 2942, a bag contains three...Ch. 6.4 - Dice If a die is rolled 30 times, there are 630...Ch. 6.4 - Dice If a die is rolled 30 times, there are 630...Ch. 6.4 - Dice If a die is rolled 30 times, there are 630...Ch. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - In Exercises 4752, calculate how many different...Ch. 6.4 - In Exercises 4752, calculate how many different...Ch. 6.4 - In Exercises 4752, calculate how many different...Ch. 6.4 - In Exercises 4752, calculate how many different...Ch. 6.4 - Prob. 52ECh. 6.4 - Itineraries Your international diplomacy trip...Ch. 6.4 - Itineraries Refer back to Exercise 53. How many...Ch. 6.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 6.4 - Prob. 56ECh. 6.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 6.4 - Prob. 58ECh. 6.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 6.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 6.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 6.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 6.4 - Prob. 63ECh. 6.4 - Day Trading Day traders typically buy and sell...Ch. 6.4 - Elimination Tournaments In an elimination...Ch. 6.4 - Elimination Tournaments In an elimination...Ch. 6.4 - Prob. 67ECh. 6.4 - Prob. 68ECh. 6.4 - Prob. 69ECh. 6.4 - Prob. 70ECh. 6.4 - Traveling Salesperson Suppose you are a...Ch. 6.4 - Prob. 72ECh. 6.4 - Prob. 73ECh. 6.4 - Prob. 74ECh. 6.4 - Prob. 75ECh. 6.4 - Prob. 76ECh. 6.4 - Prob. 77ECh. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - Prob. 80ECh. 6.4 - Prob. 81ECh. 6.4 - Prob. 82ECh. 6.4 - Prob. 83ECh. 6.4 - Which of the following represent combinations? (A)...Ch. 6.4 - Prob. 85ECh. 6.4 - Prob. 86ECh. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - Prob. 90ECh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - In Exercises 1924, consider a bag containing four...Ch. 6 - Prob. 21RECh. 6 - In Exercises 1924, consider a bag containing four...Ch. 6 - In Exercises 1924, consider a bag containing four...Ch. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Inventories OHaganBooks.com currently operates...Ch. 6 - Inventories OHaganBooks.com currently operates...Ch. 6 - Inventories OHaganBooks.com currently operates...Ch. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Customers OHaganBooks.com has two main...Ch. 6 - Online IDs As the customer base at OHaganBooks.com...Ch. 6 - Prob. 38RECh. 6 - Online IDs As the customer base at OHaganBooks.com...Ch. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RE
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