College Algebra (10th Edition)
10th Edition
ISBN: 9780321979476
Author: Michael Sullivan
Publisher: PEARSON
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Chapter 10.1, Problem 39RYK
Problems 36-39 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
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Students have asked these similar questions
R denotes the field of real numbers, Q denotes the field of rationals, and
Fp denotes the field of p elements given by integers modulo p. You may refer to general
results from lectures.
Question 1
For each non-negative integer m, let R[x]m denote the
vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m.
x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent
(a) Let vi = x, V2 =
list in R[x] 3.
(b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4)
is a basis of R[x] 3.
[8]
[6]
(c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a
linear map.
[6]
(d) Write down the matrix for the map ƒ defined in (c) with respect to the basis
(2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3.
[5]
Question 4
(a) The following matrices represent linear maps on R² with respect to an
orthonormal basis:
=
[1/√5 2/√5
[2/√5 -1/√5]
"
[1/√5 2/√5]
A =
B =
[2/√5 1/√5] 1
C =
D =
=
=
[ 1/3/5 2/35]
1/√5 2/√5
-2/√5 1/√5'
For each of the matrices A, B, C, D, state whether it represents a self-adjoint
linear map, an orthogonal linear map, both, or neither.
(b) For the quadratic form
q(x, y, z) = y² + 2xy +2yz
over R, write down a linear change of variables to u, v, w such that q in these
terms is in canonical form for Sylvester's Law of Inertia.
[6]
[4]
part b please
Chapter 10 Solutions
College Algebra (10th Edition)
Ch. 10.1 - Prob. 1AYPCh. 10.1 - Prob. 2AYPCh. 10.1 - True or false The intersection of two sets is...Ch. 10.1 - Prob. 4AYPCh. 10.1 - Prob. 5CVCh. 10.1 - If the number of elements in a set is a...Ch. 10.1 - Prob. 7CVCh. 10.1 - True or False If a task consists of a sequence of...Ch. 10.1 - Prob. 9SBCh. 10.1 - Prob. 10SB
Ch. 10.1 - If n( A )=15 , n( B )=20 , and n( AB )=10 , find...Ch. 10.1 - If n( A )=30 , n( B )=40 , and n( AB )=45 , find...Ch. 10.1 - If n( AB )=50 , n( AB )=10 , and n( B )=20 , find...Ch. 10.1 - If n( AB )=60 , n( AB )=40 , and n( A )=n( B ) ,...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - In Problems 15-22, use the information given in...Ch. 10.1 - Shirts and Ties A man has 5 shirts and 3 ties. How...Ch. 10.1 - Blouses and Skirts A woman has 5 blouses and 8...Ch. 10.1 - Four-digit Numbers How many four-digit numbers can...Ch. 10.1 - Five-digit Numbers How many five-digit numbers can...Ch. 10.1 - Analyzing Survey Data In a consumer survey of 500...Ch. 10.1 - Analyzing Survey Data In a student survey, 200...Ch. 10.1 - Analyzing Survey Data In a survey of 100 investors...Ch. 10.1 - Classifying Blood Types Human blood is classified...Ch. 10.1 - Demographics The following data represent the...Ch. 10.1 - Demographics The following data represent the...Ch. 10.1 - Stock Portfolios As a financial planner, you are...Ch. 10.1 - Make up a problem different from any found in the...Ch. 10.1 - Investigate the notion of counting as it relates...Ch. 10.1 - Problems 36-39 are based on material learned...Ch. 10.1 - Problems 36-39 are based on material learned...Ch. 10.1 - Problems 36-39 are based on material learned...Ch. 10.1 - Problems 36-39 are based on material learned...Ch. 10.2 - 0!= ; 1!= . (p. 642)Ch. 10.2 - Prob. 2AYPCh. 10.2 - Prob. 3CVCh. 10.2 - A(n) ___________ is an arrangement of r objects...Ch. 10.2 - Prob. 5CVCh. 10.2 - Prob. 6CVCh. 10.2 - In Problems 7-14, find the value of each...Ch. 10.2 - Prob. 8SBCh. 10.2 - Prob. 9SBCh. 10.2 - Prob. 10SBCh. 10.2 - Prob. 11SBCh. 10.2 - Prob. 12SBCh. 10.2 - Prob. 13SBCh. 10.2 - Prob. 14SBCh. 10.2 - Prob. 15SBCh. 10.2 - Prob. 16SBCh. 10.2 - In Problems 15-22, use formula (2) to find the...Ch. 10.2 - Prob. 18SBCh. 10.2 - Prob. 19SBCh. 10.2 - Prob. 20SBCh. 10.2 - Prob. 21SBCh. 10.2 - Prob. 22SBCh. 10.2 - List all the ordered arrangements of 5 objects...Ch. 10.2 - List all the ordered arrangements of 5 objects...Ch. 10.2 - Prob. 25AECh. 10.2 - Prob. 26AECh. 10.2 - List all the combinations of 5 objects a,b,c,d ,...Ch. 10.2 - Prob. 28AECh. 10.2 - Prob. 29AECh. 10.2 - List all the combinations of 6 objects 1, 2, 3, 4,...Ch. 10.2 - Prob. 31AECh. 10.2 - Prob. 32AECh. 10.2 - Forming Numbers How many three-digit numbers can...Ch. 10.2 - Forming Numbers How many three-digit numbers can...Ch. 10.2 - Prob. 35AECh. 10.2 - Prob. 36AECh. 10.2 - Forming Codes How many different three-letter...Ch. 10.2 - Prob. 38AECh. 10.2 - Prob. 39AECh. 10.2 - Stocks on the NASDAQ Companies whose stocks are...Ch. 10.2 - Prob. 41AECh. 10.2 - Prob. 42AECh. 10.2 - Prob. 43AECh. 10.2 - Prob. 44AECh. 10.2 - Arranging Books Five different mathematics books...Ch. 10.2 - Forming License Plate Numbers How many different...Ch. 10.2 - Prob. 47AECh. 10.2 - Prob. 48AECh. 10.2 - Prob. 49AECh. 10.2 - Prob. 50AECh. 10.2 - Forming Words How many different 9-letter words...Ch. 10.2 - Forming Words How many different 11-letter words...Ch. 10.2 - Selecting Objects An urn contains 7 white balls...Ch. 10.2 - Prob. 54AECh. 10.2 - Prob. 55AECh. 10.2 - Prob. 56AECh. 10.2 - Prob. 57AECh. 10.2 - Prob. 58AECh. 10.2 - Baseball Teams A baseball team has 15 members....Ch. 10.2 - Prob. 60AECh. 10.2 - Prob. 61AECh. 10.2 - Prob. 62AECh. 10.2 - Combination Locks A combination lock displays 50...Ch. 10.2 - Prob. 64DWCh. 10.2 - Prob. 65DWCh. 10.2 - Explain the difference between a permutation and a...Ch. 10.2 - Prob. 67RYKCh. 10.2 - Problems 67-70 are based on material learned...Ch. 10.2 - Problems 67-70 are based on material learned...Ch. 10.2 - Problems 67-70 are based on material learned...Ch. 10.3 - When the same probability is assigned to each...Ch. 10.3 - Prob. 2CVCh. 10.3 - True or False The probability of an event can...Ch. 10.3 - Prob. 4CVCh. 10.3 - In a probability model, which of the following...Ch. 10.3 - In a probability model, which of the following...Ch. 10.3 - Prob. 7SBCh. 10.3 - Determine whether the following is a probability...Ch. 10.3 - Prob. 9SBCh. 10.3 - Prob. 10SBCh. 10.3 - Prob. 11SBCh. 10.3 - In Problems 11-16, construct a probability model...Ch. 10.3 - In Problems 11-16, construct a probability model...Ch. 10.3 - In Problems 11-16, construct a probability model...Ch. 10.3 - In Problems 11-16, construct a probability model...Ch. 10.3 - Prob. 16SBCh. 10.3 - In Problems 17-22, use the following spinners to...Ch. 10.3 - In Problems 17-22, use the following spinners to...Ch. 10.3 - In Problems 17-22, use the following spinners to...Ch. 10.3 - In Problems 17-22, use the following spinners to...Ch. 10.3 - In Problems 17-22, use the following spinners to...Ch. 10.3 - In Problems 17-22, use the following spinners to...Ch. 10.3 - In Problems 23-26, consider the experiment of...Ch. 10.3 - Prob. 24SBCh. 10.3 - Prob. 25SBCh. 10.3 - Prob. 26SBCh. 10.3 - Assigning Probabilities A coin is weighted so that...Ch. 10.3 - Prob. 28SBCh. 10.3 - Prob. 29SBCh. 10.3 - Prob. 30SBCh. 10.3 - Prob. 31SBCh. 10.3 - Prob. 32SBCh. 10.3 - Prob. 33SBCh. 10.3 - For Problems 31-34, the sample space is S={...Ch. 10.3 - Prob. 35SBCh. 10.3 - Prob. 36SBCh. 10.3 - In Problems 37-40, assume equally likely outcomes....Ch. 10.3 - Prob. 38SBCh. 10.3 - In Problems 37-40, assume equally likely outcomes....Ch. 10.3 - In Problems 37-40, assume equally likely outcomes....Ch. 10.3 - For Problems 41-44, two fair dice are rolled....Ch. 10.3 - For Problems 41-44, two fair dice are rolled....Ch. 10.3 - For Problems 41-44, two fair dice are rolled....Ch. 10.3 - For Problems 41-44, two fair dice are rolled....Ch. 10.3 - Prob. 45SBCh. 10.3 - Prob. 46SBCh. 10.3 - In Problems 45-48, find the probability of the...Ch. 10.3 - Prob. 48SBCh. 10.3 - Prob. 49SBCh. 10.3 - If P( B )=0.30 , P( AB )=0.65 , and P( AB )=0.15 ,...Ch. 10.3 - Automobile Theft According to the Insurance...Ch. 10.3 - Pet Ownership According to the American Pet...Ch. 10.3 - Dog Ownership According to the American Pet...Ch. 10.3 - Prob. 54SBCh. 10.3 - Prob. 55SBCh. 10.3 - For Problems 57-60, a golf ball is selected at...Ch. 10.3 - For Problems 57-60, a golf ball is selected at...Ch. 10.3 - Prob. 58SBCh. 10.3 - Prob. 59SBCh. 10.3 - Prob. 60SBCh. 10.3 - On The Price Is Right, there is a game in which a...Ch. 10.3 - Prob. 62SBCh. 10.3 - Problems 63-66 are based on a survey of annual...Ch. 10.3 - Prob. 64SBCh. 10.3 - Prob. 65SBCh. 10.3 - Prob. 66SBCh. 10.3 - Prob. 67SBCh. 10.3 - Checkout Lines Through observation, it has been...Ch. 10.3 - Prob. 69SBCh. 10.3 - The faculty of the mathematics department at...Ch. 10.3 - Birthday Problem What is the probability that at...Ch. 10.3 - Birthday Problem What is the probability that at...Ch. 10.3 - Winning a Lottery Powerball is a multistate...Ch. 10.3 - Prob. 74RYKCh. 10.3 - Prob. 75RYKCh. 10.3 - Solve: log 5 ( x+3 )=2Ch. 10.3 - Solve the given system using matrices { 3x+y+2z=1...Ch. 10.R - Prob. 1RECh. 10.R - Prob. 2RECh. 10.R - Prob. 3RECh. 10.R - Prob. 4RECh. 10.R - Prob. 5RECh. 10.R - Prob. 6RECh. 10.R - Prob. 7RECh. 10.R - Prob. 8RECh. 10.R - Prob. 9RECh. 10.R - In Problems 10 and 11, compute the value of the...Ch. 10.R - In Problems 10 and 11, compute the value of the...Ch. 10.R - Stocking a Store A clothing store sells pure wool...Ch. 10.R - Prob. 13RECh. 10.R - Prob. 14RECh. 10.R - Choosing a Team In how many ways can a squad of 4...Ch. 10.R - Prob. 16RECh. 10.R - Prob. 17RECh. 10.R - Prob. 18RECh. 10.R - Prob. 19RECh. 10.R - Prob. 20RECh. 10.R - Forming Committees A group of 9 people is going to...Ch. 10.R - Birthday Problem For this problem, assume that a...Ch. 10.R - Unemployment According to the U.S. Bureau of Labor...Ch. 10.R - Prob. 24RECh. 10.R - Prob. 25RECh. 10.R - Prob. 26RE
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