Contemporary Mathematics For Business & Consumers, Loose-leaf Version

8th Edition

ISBN: 9781305867185

Author: Robert Brechner, Geroge Bergeman

Publisher: South-Western College Pub

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Chapter 18, Problem 3CR

Write the formula for calculating the selling price of an item when the total purchase price, including sales tax, is known. (18-3)

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Chapter 18, Problem 2CR

Chapter 18, Problem 4CR

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Each answer must be justified and all your work should appear. You will be marked on the quality of your explanations. You can discuss the problems with classmates, but you should write your solutions sepa- rately (meaning that you cannot copy the same solution from a joint blackboard, for exam- 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…

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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 18 Solutions

Contemporary Mathematics For Business & Consumers, Loose-leaf Version

Ch. 18.I - Use Exhibit 18-1 to determine the amount of sales...Ch. 18.I - Andy Bennett purchased a car for $38,600 at Auto...Ch. 18.I - At the end of a business day, the cash register at...Ch. 18.I - An archery set at The Sports Authority in Mason,...Ch. 18.I - Use Exhibit 18-1 to determine the sales tax and...Ch. 18.I - Use Exhibit 18-1 to determine the sales tax and...Ch. 18.I - Use Exhibit 18-1 to determine the sales tax and...Ch. 18.I - Use Exhibit 18-1 to determine the sales tax and...Ch. 18.I - Use Exhibit 18-1 to determine the sales tax and...Ch. 18.I - Use Exhibit 18-1 to determine the sales tax and...

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Write the formula for calculating the selling price of an item when the total purchase price, including sales tax, is known. (18-3)

Solution Summary: The author explains the formula for calculating the selling price of an item when the total purchase price, including the sale tax, is known.

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Chapter 18 Solutions