Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 17, Problem 45E
Exercises 45 through 48 refer to the following: As part of a research project, the blood pressures of 2000 patients in a hospital are recorded. The systolic blood pressures (given in millimeters) have an approximately
1. 1. Estimate the number of patients whose blood pressure was between 99 and 151 millimeters.
2. Estimate the number of patients whose blood pressure was between 112 and 151 millimeters.
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1. True or false:
(a) if E is a subspace of V, then dim(E) + dim(E) = dim(V)
(b) Let {i, n} be a basis of the vector space V, where v₁,..., Un are all eigen-
vectors for both the matrix A and the matrix B. Then, any eigenvector of A is
an eigenvector of B.
Justify.
2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1,2,-2), (1, −1, 4), (2, 1, 1)}.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show…
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1. True or false:
(a) if E is a subspace of V, then dim(E) + dim(E+) = dim(V)
(b) Let {i, n} be a basis of the vector space V, where vi,..., are all eigen-
vectors for both the matrix A and the matrix B. Then, any eigenvector of A is
an eigenvector of B.
Justify.
2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1, 2, -2), (1, −1, 4), (2, 1, 1)}.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show that P - Q is its own inverse.
4. Show that the Frobenius product on n x n-matrices,
(A, B) =
= Tr(B*A),
is an inner product, where B* denotes the Hermitian adjoint of B.
5. Show that if A and B are two n x n-matrices for which {1,..., n} is a basis of eigen-
vectors (for both A and B), then AB = BA.
Remark: It is also true that if AB = BA, then there exists a common…
Chapter 17 Solutions
Excursions In Modern Mathematics, 9th Edition
Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider a normal distribution with mean =81.2lb...Ch. 17 - Consider a normal distribution with mean =2354...Ch. 17 - Consider a normal distribution with first quartile...Ch. 17 - Consider a normal distribution with first quartile...Ch. 17 - Estimate the value of the standard deviation ...Ch. 17 - Estimate the value of the standard deviation ...
Ch. 17 - Explain why a distribution with median M=82, mean...Ch. 17 - Explain why a distribution with median M=453, mean...Ch. 17 - Explain why a distribution with =195, Q1=180 and...Ch. 17 - Explain why a distribution with M==47, Q1=35 and...Ch. 17 - A normal distribution has mean =30kg and standard...Ch. 17 - Prob. 16ECh. 17 - Prob. 17ECh. 17 - Prob. 18ECh. 17 - Prob. 19ECh. 17 - In a normal distribution with mean =83.2 and...Ch. 17 - Prob. 21ECh. 17 - Prob. 22ECh. 17 - Prob. 23ECh. 17 - Prob. 24ECh. 17 - Prob. 25ECh. 17 - In a normal distribution with standard deviation...Ch. 17 - Prob. 27ECh. 17 - Prob. 28ECh. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution defined by Fig....Ch. 17 - Consider the normal distribution defined by Fig....Ch. 17 - A normal distribution has mean =71.5in., and the...Ch. 17 - A normal distribution has standard deviation =12.3...Ch. 17 - Prob. 35ECh. 17 - Prob. 36ECh. 17 - Prob. 37ECh. 17 - A normal distribution has mean =500 and standard...Ch. 17 - In a normal distribution, what percent of the data...Ch. 17 - In a normal distribution, what percent of the data...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - An honest coin is tossed n=3600 times. Let the...Ch. 17 - Prob. 58ECh. 17 - Suppose that a random sample of n=7056 adults is...Ch. 17 - An honest die is rolled. If the roll comes out...Ch. 17 - A dishonest coin with probability of heads p=0.4...Ch. 17 - A dishonest coin with probability of heads p=0.75...Ch. 17 - Prob. 63ECh. 17 - Suppose that 1 out of every 10 plasma televisions...Ch. 17 - Prob. 65ECh. 17 - Prob. 66ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 68ECh. 17 - Prob. 69ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 71ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 73ECh. 17 - Prob. 74ECh. 17 - Prob. 75ECh. 17 - Prob. 76ECh. 17 - A dishonest coin with probability of heads p=0.1...Ch. 17 - Prob. 78ECh. 17 - In American roulette there are 18 red numbers, 18...Ch. 17 - After polling a random sample of 800 voters during...
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