EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Textbook Question
Chapter 39, Problem 31A
For Exercises 23 through 34, round the answers to 1 decimal place.
31. All dimensions are in inches. Find the shaded area of Figure 39-21.
Area
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ple).
Your work should be submitted on Moodle, before February 7 at 5 pm.
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…
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…
Question 1. Let f: XY and g: Y Z be two functions. Prove that
(1) if go f is injective, then f is injective;
(2) if go f is surjective, then g is surjective.
Question 2. Prove or disprove:
(1) The set X = {k € Z} is countable.
(2) The set X = {k EZ,nЄN} is countable.
(3) The set X = R\Q = {x ER2
countable.
Q} (the set of all irrational numbers) is
(4) The set X = {p.√2pQ} is countable.
(5) The interval X = [0,1] is countable.
Question 3. Let X = {f|f: N→ N}, the set of all functions from N to N. Prove
that X is uncountable.
Extra practice (not to be submitted).
Question. Prove the following by induction.
(1) For any nЄN, 1+3+5++2n-1 n².
(2) For any nЄ N, 1+2+3++ n = n(n+1).
Question. Write explicitly a function f: Nx N N which is bijective.
Chapter 39 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 39 - Use the Table of BlockThicknesses of a Customary...Ch. 39 - Use a digital micrometer to measure the length and...Ch. 39 - Read the setting of the metric micrometer scale in...Ch. 39 - Use an electronic vernier caliper to measure the...Ch. 39 - Prob. 5ACh. 39 - 43 is 62% of what number? Round the answer to 2...Ch. 39 - Express each of the following problems as an...Ch. 39 - Express each of the following problems as an...Ch. 39 - Express each of the following problems as an...Ch. 39 - Express each of the following problems as an...
Ch. 39 - Express each of the following problems as an...Ch. 39 - Express each of the following problems as an...Ch. 39 - Express each of the following problems as an...Ch. 39 - In the part shown in Figure 39-9, all dimensions...Ch. 39 - Find the distance between the indicated points of...Ch. 39 - What are the lengths of the following dimensions...Ch. 39 - Stock is removed from a block in two operations....Ch. 39 - Given: In Figure 39-12, s is the length of a side...Ch. 39 - Substitute the given numbers for letters and find...Ch. 39 - Prob. 20ACh. 39 - Prob. 21ACh. 39 - Prob. 22ACh. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...Ch. 39 - For Exercises 23 through 34, round the answers to...
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