A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
13th Edition
ISBN: 9780135183885
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans
Publisher: PEARSON
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Chapter 9.3A, Problem 21A
To determine
To find:
The odds in favor of rain.
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Let
2
A =
4
3
-4
0
1
(a) Show that v =
eigenvalue.
()
is an eigenvector of A and find the corresponding
(b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a)
may be useful.
(c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces.
(d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
Chapter 9 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Ch. 9.1 - Prob. 1MCCh. 9.1 - Prob. 2MCCh. 9.1 - Prob. 3MCCh. 9.1 - Prob. 4MCCh. 9.1 - Prob. 5MCCh. 9.1 - Prob. 6MCCh. 9.1 - If possible, for each of the following letters,...Ch. 9.1 - Prob. 8MCCh. 9.1 - Jose claims that if the following spinner is spun...Ch. 9.1 - Zoe is playing a game in which she draws one ball...
Ch. 9.1 - Ian and Sophia flip a fair coin ten times and...Ch. 9.1 - A certain game has four mutually exclusive...Ch. 9.1 - Prob. 13MCCh. 9.1 - A student observes the following spinner and...Ch. 9.1 - Prob. 15MCCh. 9.1 - Prob. 16MCCh. 9.1 - Prob. 17MCCh. 9.1 - Board games that use dice sometimes give children...Ch. 9.1 - Suppose the figure in exercise 14 is a is a...Ch. 9.1 - On the School Book Page on page 501, complete the...Ch. 9.1 - Mark has nine shirts in his closet as shown. If...Ch. 9.1 - Ms. Livingstons class spins the arrow on the...Ch. 9.1 - Lori has a choice of two spinners. She wants the...Ch. 9.1 - Each of the 6 faces of a fair cube is painted red,...Ch. 9.1 - Prob. 5NAEPCh. 9.1A - Consider the experiment of drawing a single card...Ch. 9.1A - The experimental probability of rolling a 4 on a...Ch. 9.1A - Each letter of the alphabet is written on a...Ch. 9.1A - The spinner shown is spun. Find the probability of...Ch. 9.1A - A card is selected from a ordinary deck of 52...Ch. 9.1A - Suppose a drawer contains six black socks, four...Ch. 9.1A - Prob. 7ACh. 9.1A - According to a weather report, there is a 30...Ch. 9.1A - A set of dolls is in a packing crate: 17 with...Ch. 9.1A - The plays generally considered the tragedies by...Ch. 9.1A - Prob. 11ACh. 9.1A - Prob. 12ACh. 9.1A - A calculus class is composed of 35 men and 45...Ch. 9.1A - A box contains five white balls, three black balls...Ch. 9.1A - Prob. 16ACh. 9.1A - If you flipped a fair coin 15 times and got 15...Ch. 9.1A - A witness identified all the digits on a license...Ch. 9.1A - Prob. 20ACh. 9.1A - If A and B are mutually exclusive, P(A)=0.3, and...Ch. 9.1A - How many times would you except to obtain a 4 on a...Ch. 9.1B - Prob. 1ACh. 9.1B - Prob. 2ACh. 9.1B - In each of the following scenarios, sketch a...Ch. 9.1B - Prob. 4ACh. 9.1B - Prob. 5ACh. 9.1B - Prob. 6ACh. 9.1B - Prob. 7ACh. 9.1B - Prob. 8ACh. 9.1B - Prob. 9ACh. 9.1B - Prob. 10ACh. 9.1B - Prob. 11ACh. 9.1B - Prob. 12ACh. 9.1B - Prob. 13ACh. 9.1B - Prob. 14ACh. 9.1B - Prob. 17ACh. 9.1B - What is the probability of choosing a continent at...Ch. 9.1B - Prob. 20ACh. 9.1B - Prob. 21ACh. 9.1B - How many times would you except to obtain a 6 on a...Ch. 9.2 - Six fair dice are thrown at the same time. If...Ch. 9.2 - A witness to a crime observed that the criminal...Ch. 9.2 - You are given three white balls, one red ball, and...Ch. 9.2 - Prob. 4MCCh. 9.2 - Prob. 5MCCh. 9.2 - Make up a game in which the players have an equal...Ch. 9.2 - How can the faces of two cubes be numbered so that...Ch. 9.2 - Mathematical Connections Design a pair of...Ch. 9.2 - An experiment consists of tossing a fair coin...Ch. 9.2 - Prob. 11MCCh. 9.2 - A student would like to know the difference...Ch. 9.2 - In response to the question, If a fair die is...Ch. 9.2 - A student is not sure when to add and when to...Ch. 9.2 - There are two boxes with different-colored balls....Ch. 9.2 - Alberto is to spin the spinners shown and compute...Ch. 9.2 - Match the following phrase to the probability that...Ch. 9.2 - A date in the month of April is chosen at random....Ch. 9.2 - Three men were walking down a street talking when...Ch. 9.2 - A roulette wheel has 38 slots around the rim; 36...Ch. 9.2 - If the roulette wheel in exercise 21 is spun 190...Ch. 9.2 - Prob. 1NAEPCh. 9.2 - Prob. 2NAEPCh. 9.2 - Prob. 3NAEPCh. 9.2 - National Assessment of Educational Progress NAEP...Ch. 9.2A - Assessment A pair of fair dice is rolled. Find the...Ch. 9.2A - Assessment a. A box contains three white balls and...Ch. 9.2A - Prob. 4ACh. 9.2A - An executive committee consisted of 10 members: 4...Ch. 9.2A - Assume the probability is 12 that a child born at...Ch. 9.2A - Prob. 7ACh. 9.2A - Assessment You roll a die twice and take the...Ch. 9.2A - Prob. 9ACh. 9.2A - If a person takes a five-question true-false test,...Ch. 9.2A - Assessment Rattlesnake and Paxson Colleges play...Ch. 9.2A - Consider the following dartboard where all...Ch. 9.2A - Prob. 13ACh. 9.2A - There are 40 employees in a certain firm. We know...Ch. 9.2A - Prob. 15ACh. 9.2A - When you toss a quarter 4 times, what is the...Ch. 9.2A - Prob. 17ACh. 9.2A - Prob. 18ACh. 9.2A - Prob. 19ACh. 9.2A - A bag contain 3 blue marbles, 4 red marbles, and 3...Ch. 9.2A - Assessment You roll a die twice. a. The sum of the...Ch. 9.2A - Prob. 22ACh. 9.2A - Prob. 23ACh. 9.2A - Prob. 24ACh. 9.2A - Following are three boxes containing balls. Draw a...Ch. 9.2B - Prob. 1ACh. 9.2B - Prob. 3ACh. 9.2B - Prob. 4ACh. 9.2B - Prob. 5ACh. 9.2B - Prob. 6ACh. 9.2B - Prob. 11ACh. 9.2B - Prob. 13ACh. 9.2B - Prob. 14ACh. 9.2B - A husband and wife discover that there is a 10...Ch. 9.2B - Prob. 16ACh. 9.2B - Prob. 17ACh. 9.2B - Prob. 21ACh. 9.2B - Prob. 22ACh. 9.2B - Assessment At her favorite coffee shop, Ashaunte...Ch. 9.2B - Assessment In box number 1, there are 4 blue...Ch. 9.3 - Prob. 1MCCh. 9.3 - Prob. 2MCCh. 9.3 - A game involves tossing two coins. A player wins...Ch. 9.3 - Prob. 4MCCh. 9.3 - Suppose we toss two fair coins. Design a fair game...Ch. 9.3 - Prob. 8MCCh. 9.3 - Prob. 9MCCh. 9.3 - At the beginning of this season, the odds listed...Ch. 9.3 - Prob. 11MCCh. 9.3 - Prob. 13MCCh. 9.3 - Prob. 14MCCh. 9.3 - Prob. 15MCCh. 9.3 - Prob. 16MCCh. 9.3 - Prob. 17MCCh. 9.3 - Prob. 18MCCh. 9.3 - Prob. 19MCCh. 9.3 - Prob. 20MCCh. 9.3 - Prob. 21MCCh. 9.3 - From a sack containing seven red marbles, eight...Ch. 9.3 - Prob. 23MCCh. 9.3 - Prob. 24MCCh. 9.3 - Prob. 25MCCh. 9.3 - Prob. 26MCCh. 9.3A - Could we use a thumb tack to simulate the birth of...Ch. 9.3A - Prob. 2ACh. 9.3A - Prob. 4ACh. 9.3A - Prob. 5ACh. 9.3A - Prob. 6ACh. 9.3A - Pick a block of two digits from the random-number...Ch. 9.3A - Prob. 8ACh. 9.3A - Prob. 10ACh. 9.3A - Prob. 11ACh. 9.3A - Prob. 12ACh. 9.3A - If the probability of a boys being born is 12, and...Ch. 9.3A - If the odds against Deborahs winning first prize...Ch. 9.3A - If the probability of the event that a randomly...Ch. 9.3A - Prob. 16ACh. 9.3A - Prob. 17ACh. 9.3A - Prob. 18ACh. 9.3A - Prob. 19ACh. 9.3A - Prob. 20ACh. 9.3A - Prob. 21ACh. 9.3A - Determine each of the following. a. What are the...Ch. 9.3A - Suppose five quarters, five dimes, fives nickels,...Ch. 9.3A - If the odds in favor of Fast Leg winning a horse...Ch. 9.3A - Prob. 25ACh. 9.3A - Carina is playing a game that costs 10 to play....Ch. 9.3A - Prob. 27ACh. 9.3A - Assessment If the probability of spilling soup on...Ch. 9.3A - Assessment A bag of grass seed is advertised as...Ch. 9.3A - Suppose you invented a game based on taking the...Ch. 9.3B - How could we use a spinner as shown below to...Ch. 9.3B - How could we use a random-digit generator or...Ch. 9.3B - Prob. 3ACh. 9.3B - Prob. 4ACh. 9.3B - Prob. 5ACh. 9.3B - Use a random-number table to estimate the...Ch. 9.3B - Prob. 10ACh. 9.3B - Prob. 11ACh. 9.3B - Prob. 12ACh. 9.3B - Prob. 13ACh. 9.3B - Prob. 14ACh. 9.3B - Two dice are rolled; find the odds against rolling...Ch. 9.3B - a. What are the odds in favor of randomly drawing...Ch. 9.3B - The probability that a person passes a test is 75....Ch. 9.3B - Prob. 18ACh. 9.3B - Prob. 19ACh. 9.3B - Determine each of the following. a. What are the...Ch. 9.3B - Prob. 21ACh. 9.3B - On a roulette wheel, half of the slots numbered 1...Ch. 9.3B - Suppose someone was playing the following dice...Ch. 9.3B - Suppose a standard six-sided die is rolled and you...Ch. 9.3B - Prob. 26ACh. 9.3B - Prob. 27ACh. 9.3B - Prob. 28ACh. 9.3B - Prob. 29ACh. 9.3B - Dean is playing a game that costs 10 to play. He...Ch. 9.4 - The terms Fundamental Counting Principle,...Ch. 9.4 - A bicycle lock has three reels, each of which...Ch. 9.4 - In how many ways can five couples be seated in a...Ch. 9.4 - Prob. 5MCCh. 9.4 - Prob. 6MCCh. 9.4 - Prob. 7MCCh. 9.4 - Prob. 8MCCh. 9.4 - Combination locks are poorly named, mainly because...Ch. 9.4 - A student does not understand the meaning of 4P0 ....Ch. 9.4 - Prob. 11MCCh. 9.4 - Prob. 12MCCh. 9.4 - Prob. 13MCCh. 9.4 - If two regular dice are tossed, what is...Ch. 9.4 - On a roulette wheel, the probability of the event...Ch. 9.4 - Prob. 1NAEPCh. 9.4 - Prob. 2NAEPCh. 9.4A - Prob. 1ACh. 9.4A - Prob. 2ACh. 9.4A - The eighth grade class at a grade school has 16...Ch. 9.4A - Prob. 4ACh. 9.4A - Carlins Pizza House offer 3 kinds of salad, 15...Ch. 9.4A - Prob. 6ACh. 9.4A - Find the number of ways to arrange the letter in...Ch. 9.4A - Prob. 8ACh. 9.4A - Assume a class has 30 members a. In how many ways...Ch. 9.4A - Prob. 10ACh. 9.4A - At a party, 28 handshakes took place. Each person...Ch. 9.4A - Prob. 12ACh. 9.4A - Postal codes in Canada consist of three letters...Ch. 9.4A - Baskin-Robbins advertises 31 flavors of ice cream....Ch. 9.4A - Prob. 15ACh. 9.4A - Prob. 16ACh. 9.4A - Prob. 17ACh. 9.4A - A five-volume numbered set of books is placed...Ch. 9.4A - Prob. 19ACh. 9.4A - Prob. 20ACh. 9.4A - From a group of 10 boys and 12 girls, a committee...Ch. 9.4A - From a group 20 Britons, 21 Italians, and 4 Danes,...Ch. 9.4A - Prob. 23ACh. 9.4A - A company is setting up four-digit ID numbers for...Ch. 9.4A - Your English teacher asks that you read any three...Ch. 9.4A - Prob. 26ACh. 9.4B - Prob. 1ACh. 9.4B - Prob. 2ACh. 9.4B - Assessment Radio stations in the United States...Ch. 9.4B - Prob. 5ACh. 9.4B - Find the number of ways to arrange the letters in...Ch. 9.4B - Prob. 7ACh. 9.4B - Prob. 8ACh. 9.4B - Prob. 10ACh. 9.4B - How many different 12-person juries can be...Ch. 9.4B - Prob. 12ACh. 9.4B - A club selects an executive committee of 5 and...Ch. 9.4B - Prob. 18ACh. 9.4B - A committee of three people is selected at random...Ch. 9.4B - Prob. 20ACh. 9.4B - Prob. 21ACh. 9.4B - Jackson has 20 books, but has space for only 12 on...Ch. 9.4B - Prob. 23ACh. 9.4B - In how many ways can a group of 9 people stand in...Ch. 9.4B - How many arrangements can be made from the letters...Ch. 9.CR - Prob. 1CRCh. 9.CR - Prob. 2CRCh. 9.CR - Prob. 3CRCh. 9.CR - Art works as a clown on weekends. He has three...Ch. 9.CR - Prob. 5CRCh. 9.CR - Prob. 6CRCh. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - Prob. 10CRCh. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - Prob. 13CRCh. 9.CR - A game consists of rolling two dice. Rolling...Ch. 9.CR - Prob. 15CRCh. 9.CR - In a special raffle, a ticket costs 2. You mark...Ch. 9.CR - Prob. 17CRCh. 9.CR - Prob. 18CRCh. 9.CR - Prob. 19CRCh. 9.CR - Prob. 20CRCh. 9.CR - Prob. 21CRCh. 9.CR - Prob. 22CRCh. 9.CR - Prob. 23CRCh. 9.CR - Prob. 24CRCh. 9.CR - Prob. 25CRCh. 9.CR - Prob. 26CRCh. 9.CR - Prob. 28CRCh. 9.CR - Suppose you spin a spinner and then roll a die....Ch. 9.CR - Prob. 30CRCh. 9.CR - Prob. 31CRCh. 9.CR - Prob. 32CRCh. 9.CR - Prob. 33CRCh. 9.CR - Prob. 34CRCh. 9.CR - Prob. 35CRCh. 9.CR - Prob. 36CRCh. 9.CR - Prob. 37CRCh. 9.CR - Prob. 38CRCh. 9.CR - Prob. 39CRCh. 9 - Now Try This Use StatCrunch or another coin...Ch. 9 - NOW TRY THIS a. In an experiment of tossing a fair...Ch. 9 - Prob. 4NTCh. 9 - Prob. 6NTCh. 9 - Prob. 7NTCh. 9 - Prob. 8NTCh. 9 - Prob. 9NT
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