College Algebra Enhanced with Graphing Utilities (7th Edition) (Sullivan Enhanced with Graphing Utilities Series)
College Algebra Enhanced with Graphing Utilities (7th Edition) (Sullivan Enhanced with Graphing Utilities Series)
7th Edition
ISBN: 9780134111315
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Chapter 4, Problem 4CR
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1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.
Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]
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]

Chapter 4 Solutions

College Algebra Enhanced with Graphing Utilities (7th Edition) (Sullivan Enhanced with Graphing Utilities Series)

Ch. 4.1 - Prob. 11AYUCh. 4.1 - Prob. 12AYUCh. 4.1 - Prob. 13AYUCh. 4.1 - Prob. 14AYUCh. 4.1 - Prob. 15AYUCh. 4.1 - Prob. 16AYUCh. 4.1 - Prob. 17AYUCh. 4.1 - Prob. 18AYUCh. 4.1 - Prob. 19AYUCh. 4.1 - Prob. 20AYUCh. 4.1 - Prob. 21AYUCh. 4.1 - Prob. 22AYUCh. 4.1 - Prob. 23AYUCh. 4.1 - Prob. 24AYUCh. 4.1 - Prob. 25AYUCh. 4.1 - Prob. 26AYUCh. 4.1 - Prob. 27AYUCh. 4.1 - Prob. 28AYUCh. 4.1 - Prob. 29AYUCh. 4.1 - Prob. 30AYUCh. 4.1 - Prob. 31AYUCh. 4.1 - Prob. 32AYUCh. 4.1 - Prob. 33AYUCh. 4.1 - Prob. 34AYUCh. 4.1 - Prob. 35AYUCh. 4.1 - Prob. 36AYUCh. 4.1 - Prob. 37AYUCh. 4.1 - Prob. 38AYUCh. 4.1 - Prob. 39AYUCh. 4.1 - Prob. 40AYUCh. 4.1 - Prob. 41AYUCh. 4.1 - Prob. 42AYUCh. 4.1 - Prob. 43AYUCh. 4.1 - Prob. 44AYUCh. 4.1 - Prob. 45AYUCh. 4.1 - Prob. 46AYUCh. 4.1 - 47. Cost Function The simplest cost function is...Ch. 4.1 - Prob. 48AYUCh. 4.1 - Prob. 49AYUCh. 4.1 - 50. International Call Plan A cell phone company...Ch. 4.1 - Prob. 51AYUCh. 4.1 - Prob. 52AYUCh. 4.1 - 53. Which of the following functions might have...Ch. 4.1 - 54. Which of the following functions might have...Ch. 4.1 - Prob. 55AYUCh. 4.1 - Prob. 56AYUCh. 4.1 - Prob. 57AYUCh. 4.1 - Prob. 58AYUCh. 4.1 - Prob. 59AYUCh. 4.1 - Prob. 60AYUCh. 4.2 - Prob. 1AYUCh. 4.2 - Prob. 2AYUCh. 4.2 - Prob. 3AYUCh. 4.2 - Prob. 4AYUCh. 4.2 - Prob. 5AYUCh. 4.2 - Prob. 6AYUCh. 4.2 - Prob. 7AYUCh. 4.2 - Prob. 8AYUCh. 4.2 - Prob. 9AYUCh. 4.2 - Prob. 10AYUCh. 4.2 - Prob. 11AYUCh. 4.2 - Prob. 12AYUCh. 4.2 - Prob. 13AYUCh. 4.2 - Prob. 14AYUCh. 4.2 - Prob. 15AYUCh. 4.2 - Prob. 16AYUCh. 4.2 - Prob. 17AYUCh. 4.2 - Prob. 18AYUCh. 4.2 - Prob. 19AYUCh. 4.2 - Prob. 20AYUCh. 4.2 - Prob. 21AYUCh. 4.2 - Prob. 22AYUCh. 4.2 - Prob. 23AYUCh. 4.2 - Prob. 24AYUCh. 4.2 - Prob. 25AYUCh. 4.2 - Prob. 26AYUCh. 4.2 - Prob. 27AYUCh. 4.2 - Prob. 28AYUCh. 4.2 - Prob. 29AYUCh. 4.2 - Prob. 30AYUCh. 4.2 - Prob. 31AYUCh. 4.3 - 1. List the intercepts of the equation . Ch. 4.3 - Prob. 2AYUCh. 4.3 - Prob. 3AYUCh. 4.3 - Prob. 4AYUCh. 4.3 - Prob. 5AYUCh. 4.3 - 6. The vertical line passing through the vertex of...Ch. 4.3 - Prob. 7AYUCh. 4.3 - Prob. 8AYUCh. 4.3 - Prob. 9AYUCh. 4.3 - Prob. 10AYUCh. 4.3 - Prob. 11AYUCh. 4.3 - Prob. 12AYUCh. 4.3 - In Problems 13-20, match each graph to one the...Ch. 4.3 - Prob. 14AYUCh. 4.3 - In Problems 13-20, match each graph to one the...Ch. 4.3 - Prob. 16AYUCh. 4.3 - In Problems 13-20, match each graph to one the...Ch. 4.3 - Prob. 18AYUCh. 4.3 - In Problems 13-20, match each graph to one the...Ch. 4.3 - In Problems 13-20, match each graph to one the...Ch. 4.3 - Prob. 21AYUCh. 4.3 - Prob. 22AYUCh. 4.3 - Prob. 23AYUCh. 4.3 - Prob. 24AYUCh. 4.3 - Prob. 25AYUCh. 4.3 - Prob. 26AYUCh. 4.3 - Prob. 27AYUCh. 4.3 - Prob. 28AYUCh. 4.3 - Prob. 29AYUCh. 4.3 - Prob. 30AYUCh. 4.3 - Prob. 31AYUCh. 4.3 - Prob. 32AYUCh. 4.3 - Prob. 33AYUCh. 4.3 - Prob. 34AYUCh. 4.3 - Prob. 35AYUCh. 4.3 - Prob. 36AYUCh. 4.3 - Prob. 37AYUCh. 4.3 - Prob. 38AYUCh. 4.3 - Prob. 39AYUCh. 4.3 - Prob. 40AYUCh. 4.3 - In Problems 33-48, (a) graph each quadratic...Ch. 4.3 - Prob. 42AYUCh. 4.3 - Prob. 43AYUCh. 4.3 - Prob. 44AYUCh. 4.3 - Prob. 45AYUCh. 4.3 - Prob. 46AYUCh. 4.3 - Prob. 47AYUCh. 4.3 - Prob. 48AYUCh. 4.3 - In Problems 49-54, determine the quadratic...Ch. 4.3 - Prob. 50AYUCh. 4.3 - Prob. 51AYUCh. 4.3 - Prob. 52AYUCh. 4.3 - Prob. 53AYUCh. 4.3 - Prob. 54AYUCh. 4.3 - In Problem 55-62, determine, without graphing,...Ch. 4.3 - Prob. 56AYUCh. 4.3 - Prob. 57AYUCh. 4.3 - Prob. 58AYUCh. 4.3 - Prob. 59AYUCh. 4.3 - Prob. 60AYUCh. 4.3 - Prob. 61AYUCh. 4.3 - Prob. 62AYUCh. 4.3 - Prob. 63AYUCh. 4.3 - Prob. 64AYUCh. 4.3 - Prob. 65AYUCh. 4.3 - Prob. 66AYUCh. 4.3 - Prob. 67AYUCh. 4.3 - Prob. 68AYUCh. 4.3 - Prob. 69AYUCh. 4.3 - Prob. 70AYUCh. 4.3 - Prob. 71AYUCh. 4.3 - Prob. 72AYUCh. 4.3 - Prob. 73AYUCh. 4.3 - In Problems 63-70, (a) graph each function. (b)...Ch. 4.3 - Prob. 75AYUCh. 4.3 - Prob. 76AYUCh. 4.3 - In Problems 73-78, for the given functions f and...Ch. 4.3 - Prob. 78AYUCh. 4.3 - Prob. 79AYUCh. 4.3 - Prob. 80AYUCh. 4.3 - Prob. 81AYUCh. 4.3 - Prob. 82AYUCh. 4.3 - Prob. 83AYUCh. 4.3 - Prob. 84AYUCh. 4.3 - Prob. 85AYUCh. 4.3 - Prob. 86AYUCh. 4.3 - Prob. 87AYUCh. 4.3 - Prob. 88AYUCh. 4.3 - Prob. 89AYUCh. 4.3 - Prob. 90AYUCh. 4.3 - 87. Minimizing Marginal Cost The marginal cost of...Ch. 4.3 - Prob. 92AYUCh. 4.3 - Prob. 93AYUCh. 4.3 - 90. Business The daily revenue R achieved by...Ch. 4.3 - Prob. 95AYUCh. 4.3 - 92. Birth Rate of Unmarried Women In the United...Ch. 4.3 - Prob. 97AYUCh. 4.3 - Prob. 98AYUCh. 4.3 - Prob. 99AYUCh. 4.3 - Prob. 100AYUCh. 4.3 - Prob. 101AYUCh. 4.3 - Prob. 102AYUCh. 4.3 - Prob. 103AYUCh. 4.3 - Prob. 104AYUCh. 4.3 - Prob. 105AYUCh. 4.3 - Prob. 106AYUCh. 4.3 - Prob. 107AYUCh. 4.3 - Prob. 108AYUCh. 4.4 - 1. Translate the following sentence into a...Ch. 4.4 - Prob. 2AYUCh. 4.4 - Prob. 3AYUCh. 4.4 - 4. Maximizing Revenue The price p (in dollars) and...Ch. 4.4 - 5. Maximizing Revenue The price p (in dollars) and...Ch. 4.4 - 6. Maximizing Revenue The price p (in dollars) and...Ch. 4.4 - 7. Enclosing a Rectangular Field David has 400...Ch. 4.4 - 8. Enclosing a Rectangular Field Beth has 3000...Ch. 4.4 - Prob. 9AYUCh. 4.4 - Prob. 10AYUCh. 4.4 - Prob. 11AYUCh. 4.4 - 12. Analyzing the Motion of a Projectile A...Ch. 4.4 - Prob. 13AYUCh. 4.4 - Prob. 14AYUCh. 4.4 - 15. Constructing Rain Gutters A rain gutter is to...Ch. 4.4 - 16. Norman Windows A Norman window has the shape...Ch. 4.4 - 17. Constructing a Stadium A track-and-field...Ch. 4.4 - Prob. 18AYUCh. 4.4 - Prob. 19AYUCh. 4.4 - Prob. 20AYUCh. 4.4 - Prob. 21AYUCh. 4.4 - Prob. 22AYUCh. 4.4 - Prob. 23AYUCh. 4.4 - Prob. 24AYUCh. 4.4 - Prob. 25AYUCh. 4.4 - Prob. 26AYUCh. 4.4 - Prob. 27AYUCh. 4.4 - Prob. 28AYUCh. 4.4 - Prob. 29AYUCh. 4.4 - Prob. 30AYUCh. 4.4 - 31. Refer to Example 1 in this section. Notice...Ch. 4.4 - Prob. 32AYUCh. 4.4 - Prob. 33AYUCh. 4.4 - Prob. 34AYUCh. 4.4 - Prob. 35AYUCh. 4.5 - Prob. 1AYUCh. 4.5 - Prob. 2AYUCh. 4.5 - Prob. 3AYUCh. 4.5 - Prob. 4AYUCh. 4.5 - Prob. 5AYUCh. 4.5 - Prob. 6AYUCh. 4.5 - Prob. 7AYUCh. 4.5 - Prob. 8AYUCh. 4.5 - Prob. 9AYUCh. 4.5 - Prob. 10AYUCh. 4.5 - Prob. 11AYUCh. 4.5 - Prob. 12AYUCh. 4.5 - Prob. 13AYUCh. 4.5 - Prob. 14AYUCh. 4.5 - Prob. 15AYUCh. 4.5 - Prob. 16AYUCh. 4.5 - Prob. 17AYUCh. 4.5 - Prob. 18AYUCh. 4.5 - Prob. 19AYUCh. 4.5 - Prob. 20AYUCh. 4.5 - Prob. 21AYUCh. 4.5 - Prob. 22AYUCh. 4.5 - Prob. 23AYUCh. 4.5 - Prob. 24AYUCh. 4.5 - Prob. 25AYUCh. 4.5 - Prob. 26AYUCh. 4.5 - Prob. 27AYUCh. 4.5 - Prob. 28AYUCh. 4.5 - Prob. 29AYUCh. 4.5 - Prob. 30AYUCh. 4.5 - Prob. 31AYUCh. 4.5 - Prob. 32AYUCh. 4.5 - Prob. 33AYUCh. 4.5 - Prob. 34AYUCh. 4.5 - Prob. 35AYUCh. 4.5 - Prob. 36AYUCh. 4.5 - Prob. 37AYUCh. 4.5 - Prob. 38AYUCh. 4.5 - Prob. 39AYUCh. 4.5 - Prob. 40AYUCh. 4.5 - Prob. 41AYUCh. 4.5 - Prob. 42AYUCh. 4.5 - Prob. 43AYUCh. 4.5 - Prob. 44AYUCh. 4.5 - Prob. 45AYUCh. 4.5 - Prob. 46AYUCh. 4.5 - Prob. 47AYUCh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 1CTCh. 4 - Prob. 2CTCh. 4 - Prob. 3CTCh. 4 - Prob. 4CTCh. 4 - Prob. 5CTCh. 4 - Prob. 6CTCh. 4 - Prob. 7CTCh. 4 - Prob. 8CTCh. 4 - Prob. 9CTCh. 4 - Prob. 10CTCh. 4 - Prob. 11CTCh. 4 - Prob. 1CRCh. 4 - Prob. 2CRCh. 4 - Prob. 3CRCh. 4 - Prob. 4CRCh. 4 - Prob. 5CRCh. 4 - Prob. 6CRCh. 4 - Prob. 7CRCh. 4 - Prob. 8CRCh. 4 - Prob. 9CRCh. 4 - Prob. 10CRCh. 4 - Prob. 11CRCh. 4 - Prob. 12CRCh. 4 - Prob. 13CRCh. 4 - Prob. 14CRCh. 4 - For the graph of the function f, Find the domain...
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