EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Textbook Question
Chapter 9, Problem 47A
Write these words as numbers.
47. fourteen and five hundred thousandths
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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…
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 9 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 9 - Use Figure 9-4 to answer Exercises 16. All...Ch. 9 - Use Figure 9-4 to answer Exercises 16. All...Ch. 9 - Use Figure 9-4 to answer Exercises 16. All...Ch. 9 - Use Figure 9-4 to answer Exercises 16. All...Ch. 9 - Use Figure 9-4 to answer Exercises 16. All...Ch. 9 - Use Figure 9-4 to answer Exercises 16. All...Ch. 9 - Find the decimal value of each of the distances A,...Ch. 9 - Find the decimal value of each of the distances A,...Ch. 9 - Find the decimal value of each of the distances A,...Ch. 9 - In each of the following exercises, the value on...
Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - In each of the following exercises, the value on...Ch. 9 - Write these numbers as words. 20. 0.064Ch. 9 - Write these numbers as words. 21. 0.007Ch. 9 - Write these numbers as words. 22. 0.132Ch. 9 - Write these numbers as words. 23. 0.0035Ch. 9 - Write these numbers as words. 24. 0.108Ch. 9 - Write these numbers as words. 25. 1.5Ch. 9 - Write these numbers as words. 26. 10.37Ch. 9 - Write these numbers as words. 27. 16.0007Ch. 9 - Write these numbers as words. 28. 4.0012Ch. 9 - Write these numbers as words. 29. 13.103Ch. 9 - Write these words as numbers. 30. eighty-four...Ch. 9 - Write these words as numbers. 31. three tenthsCh. 9 - Write these words as numbers. 32. forty-three and...Ch. 9 - Write these words as numbers. 33. four and five...Ch. 9 - Write these words as numbers. 34. thirty-five...Ch. 9 - Write these words as numbers. 35. ten and two...Ch. 9 - Write these words as numbers. 36. five and one...Ch. 9 - Write these words as numbers. 37. twenty and...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these numbers as words using the alternative...Ch. 9 - Write these words as numbers. 46. forty-three and...Ch. 9 - Write these words as numbers. 47. fourteen and...Ch. 9 - Write these words as numbers. 48. thirty-seven and...Ch. 9 - Write these words as numbers. 49. one hundred six...Ch. 9 - Write these words as numbers. 50. seventy-six...Ch. 9 - Write these words as numbers. 51. four and one...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...Ch. 9 - Each of the following common fractions has a...
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