Pearson eText Algebra and Trigonometry -- Instant Access (Pearson+)
11th Edition
ISBN: 9780136872689
Author: Michael Sullivan
Publisher: PEARSON+
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Textbook Question
Chapter 5.3, Problem 33AYU
In problems 33-44, (a) graph the rational function using transormations, (b) use the final graph to find the domain and range, and (c) use the graph to list any vertical, horizontal, or oblique asymptotes.
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Chapter 5 Solutions
Pearson eText Algebra and Trigonometry -- Instant Access (Pearson+)
Ch. 5.1 - Prob. 1AYUCh. 5.1 - Prob. 2AYUCh. 5.1 - Prob. 3AYUCh. 5.1 - Prob. 4AYUCh. 5.1 - Prob. 5AYUCh. 5.1 - Prob. 6AYUCh. 5.1 - Prob. 7AYUCh. 5.1 - Prob. 8AYUCh. 5.1 - Prob. 9AYUCh. 5.1 - Prob. 10AYU
Ch. 5.1 - Prob. 11AYUCh. 5.1 - Prob. 12AYUCh. 5.1 - Prob. 13AYUCh. 5.1 - Prob. 14AYUCh. 5.1 - Prob. 15AYUCh. 5.1 - Prob. 16AYUCh. 5.1 - Prob. 17AYUCh. 5.1 - Prob. 18AYUCh. 5.1 - Prob. 19AYUCh. 5.1 - Prob. 20AYUCh. 5.1 - Prob. 21AYUCh. 5.1 - Prob. 22AYUCh. 5.1 - Prob. 23AYUCh. 5.1 - Prob. 24AYUCh. 5.1 - Prob. 25AYUCh. 5.1 - Prob. 26AYUCh. 5.1 - Prob. 27AYUCh. 5.1 - Prob. 28AYUCh. 5.1 - Prob. 29AYUCh. 5.1 - Prob. 30AYUCh. 5.1 - Prob. 31AYUCh. 5.1 - Prob. 32AYUCh. 5.1 - Prob. 33AYUCh. 5.1 - Prob. 34AYUCh. 5.1 - Prob. 35AYUCh. 5.1 - Prob. 36AYUCh. 5.1 - Prob. 37AYUCh. 5.1 - Prob. 38AYUCh. 5.1 - Prob. 39AYUCh. 5.1 - Prob. 40AYUCh. 5.1 - Prob. 41AYUCh. 5.1 - Prob. 42AYUCh. 5.1 - Prob. 43AYUCh. 5.1 - Prob. 44AYUCh. 5.1 - Prob. 45AYUCh. 5.1 - Prob. 46AYUCh. 5.1 - Prob. 47AYUCh. 5.1 - Prob. 48AYUCh. 5.1 - Prob. 49AYUCh. 5.1 - Prob. 50AYUCh. 5.1 - Prob. 51AYUCh. 5.1 - Prob. 52AYUCh. 5.1 - Prob. 53AYUCh. 5.1 - Prob. 54AYUCh. 5.1 - Prob. 55AYUCh. 5.1 - Prob. 56AYUCh. 5.1 - Prob. 57AYUCh. 5.1 - Prob. 58AYUCh. 5.1 - 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Prob. 3AYUCh. 5.2 - Prob. 4AYUCh. 5.2 - Prob. 5AYUCh. 5.2 - Prob. 6AYUCh. 5.2 - Prob. 7AYUCh. 5.2 - Prob. 8AYUCh. 5.2 - Prob. 9AYUCh. 5.2 - Prob. 10AYUCh. 5.2 - Prob. 11AYUCh. 5.2 - Prob. 12AYUCh. 5.2 - Prob. 13AYUCh. 5.2 - Prob. 14AYUCh. 5.2 - Prob. 15AYUCh. 5.2 - Prob. 16AYUCh. 5.2 - Prob. 17AYUCh. 5.2 - Prob. 18AYUCh. 5.2 - Prob. 19AYUCh. 5.2 - Prob. 20AYUCh. 5.2 - Prob. 21AYUCh. 5.2 - Prob. 22AYUCh. 5.2 - Prob. 23AYUCh. 5.2 - Prob. 24AYUCh. 5.2 - Prob. 25AYUCh. 5.2 - Prob. 26AYUCh. 5.2 - Prob. 27AYUCh. 5.2 - Prob. 28AYUCh. 5.2 - Prob. 29AYUCh. 5.2 - Prob. 30AYUCh. 5.2 - Prob. 31AYUCh. 5.2 - Prob. 32AYUCh. 5.2 - Prob. 33AYUCh. 5.2 - Prob. 34AYUCh. 5.2 - Prob. 35AYUCh. 5.2 - Prob. 36AYUCh. 5.2 - Prob. 37AYUCh. 5.2 - Prob. 38AYUCh. 5.2 - Prob. 39AYUCh. 5.2 - Prob. 40AYUCh. 5.2 - Prob. 41AYUCh. 5.2 - Prob. 42AYUCh. 5.2 - Prob. 43AYUCh. 5.2 - Prob. 44AYUCh. 5.2 - Prob. 45AYUCh. 5.2 - Prob. 46AYUCh. 5.2 - Prob. 47AYUCh. 5.2 - Prob. 48AYUCh. 5.2 - Prob. 49AYUCh. 5.2 - Prob. 50AYUCh. 5.2 - Prob. 51AYUCh. 5.2 - Prob. 52AYUCh. 5.2 - Prob. 53AYUCh. 5.2 - Prob. 54AYUCh. 5.2 - Prob. 55AYUCh. 5.2 - Prob. 56AYUCh. 5.2 - Prob. 57AYUCh. 5.2 - Prob. 58AYUCh. 5.2 - Prob. 59AYUCh. 5.3 - Prob. 1AYUCh. 5.3 - Prob. 2AYUCh. 5.3 - Prob. 3AYUCh. 5.3 - Prob. 4AYUCh. 5.3 - Prob. 5AYUCh. 5.3 - Prob. 6AYUCh. 5.3 - Prob. 7AYUCh. 5.3 - Prob. 8AYUCh. 5.3 - Prob. 9AYUCh. 5.3 - Prob. 10AYUCh. 5.3 - Prob. 11AYUCh. 5.3 - Prob. 12AYUCh. 5.3 - Prob. 13AYUCh. 5.3 - Prob. 14AYUCh. 5.3 - Prob. 15AYUCh. 5.3 - Prob. 16AYUCh. 5.3 - Prob. 17AYUCh. 5.3 - Prob. 18AYUCh. 5.3 - Prob. 19AYUCh. 5.3 - Prob. 20AYUCh. 5.3 - Prob. 21AYUCh. 5.3 - Prob. 22AYUCh. 5.3 - Prob. 23AYUCh. 5.3 - Prob. 24AYUCh. 5.3 - Prob. 25AYUCh. 5.3 - Prob. 26AYUCh. 5.3 - Prob. 27AYUCh. 5.3 - Prob. 28AYUCh. 5.3 - Prob. 29AYUCh. 5.3 - Prob. 30AYUCh. 5.3 - Prob. 31AYUCh. 5.3 - Prob. 32AYUCh. 5.3 - In problems 33-44, (a) graph the rational function...Ch. 5.3 - Prob. 34AYUCh. 5.3 - Prob. 35AYUCh. 5.3 - Prob. 36AYUCh. 5.3 - Prob. 37AYUCh. 5.3 - Prob. 38AYUCh. 5.3 - Prob. 39AYUCh. 5.3 - Prob. 40AYUCh. 5.3 - Prob. 41AYUCh. 5.3 - Prob. 42AYUCh. 5.3 - Prob. 43AYUCh. 5.3 - Prob. 44AYUCh. 5.3 - Prob. 45AYUCh. 5.3 - Prob. 46AYUCh. 5.3 - Prob. 47AYUCh. 5.3 - Prob. 48AYUCh. 5.3 - Prob. 49AYUCh. 5.3 - Prob. 50AYUCh. 5.3 - Prob. 51AYUCh. 5.3 - Prob. 52AYUCh. 5.3 - Prob. 53AYUCh. 5.3 - Prob. 54AYUCh. 5.3 - Prob. 55AYUCh. 5.3 - Prob. 56AYUCh. 5.3 - Prob. 57AYUCh. 5.3 - Prob. 58AYUCh. 5.3 - Prob. 59AYUCh. 5.3 - Prob. 60AYUCh. 5.3 - Prob. 61AYUCh. 5.3 - Prob. 62AYUCh. 5.3 - Prob. 63AYUCh. 5.3 - Prob. 64AYUCh. 5.3 - Prob. 65AYUCh. 5.3 - Prob. 66AYUCh. 5.3 - Prob. 67AYUCh. 5.3 - Prob. 68AYUCh. 5.3 - Prob. 69AYUCh. 5.3 - Prob. 70AYUCh. 5.3 - Prob. 71AYUCh. 5.3 - Prob. 72AYUCh. 5.3 - Prob. 73AYUCh. 5.3 - Prob. 74AYUCh. 5.3 - Prob. 75AYUCh. 5.3 - Prob. 76AYUCh. 5.4 - Prob. 1AYUCh. 5.4 - Prob. 2AYUCh. 5.4 - Prob. 3AYUCh. 5.4 - Prob. 4AYUCh. 5.4 - Prob. 5AYUCh. 5.4 - Prob. 6AYUCh. 5.4 - Prob. 7AYUCh. 5.4 - Prob. 8AYUCh. 5.4 - Prob. 9AYUCh. 5.4 - Prob. 10AYUCh. 5.4 - Prob. 11AYUCh. 5.4 - 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Prob. 60AYUCh. 5.4 - Prob. 61AYUCh. 5.4 - Prob. 62AYUCh. 5.4 - Prob. 63AYUCh. 5.4 - Prob. 64AYUCh. 5.4 - Prob. 65AYUCh. 5.4 - Prob. 66AYUCh. 5.4 - Prob. 67AYUCh. 5.4 - Prob. 68AYUCh. 5.4 - Prob. 69AYUCh. 5.4 - Prob. 70AYUCh. 5.4 - Prob. 71AYUCh. 5.4 - Prob. 72AYUCh. 5.4 - Prob. 73AYUCh. 5.4 - Prob. 74AYUCh. 5.4 - Prob. 75AYUCh. 5.4 - Prob. 76AYUCh. 5.4 - Prob. 77AYUCh. 5.4 - Prob. 78AYUCh. 5.4 - Prob. 79AYUCh. 5.4 - Prob. 80AYUCh. 5.4 - Prob. 81AYUCh. 5.4 - Prob. 82AYUCh. 5.4 - Prob. 83AYUCh. 5.4 - Prob. 84AYUCh. 5.4 - Prob. 85AYUCh. 5.5 - Prob. 1AYUCh. 5.5 - Prob. 2AYUCh. 5.5 - Prob. 3AYUCh. 5.5 - Prob. 4AYUCh. 5.5 - Prob. 5AYUCh. 5.5 - Prob. 6AYUCh. 5.5 - Prob. 7AYUCh. 5.5 - Prob. 8AYUCh. 5.5 - Prob. 9AYUCh. 5.5 - Prob. 10AYUCh. 5.5 - Prob. 11AYUCh. 5.5 - Prob. 12AYUCh. 5.5 - Prob. 13AYUCh. 5.5 - Prob. 14AYUCh. 5.5 - Prob. 15AYUCh. 5.5 - Prob. 16AYUCh. 5.5 - Prob. 17AYUCh. 5.5 - Prob. 18AYUCh. 5.5 - Prob. 19AYUCh. 5.5 - Prob. 20AYUCh. 5.5 - Prob. 21AYUCh. 5.5 - Prob. 22AYUCh. 5.5 - Prob. 23AYUCh. 5.5 - Prob. 24AYUCh. 5.5 - Prob. 25AYUCh. 5.5 - Prob. 26AYUCh. 5.5 - Prob. 27AYUCh. 5.5 - Prob. 28AYUCh. 5.5 - Prob. 29AYUCh. 5.5 - Prob. 30AYUCh. 5.5 - Prob. 31AYUCh. 5.5 - Prob. 32AYUCh. 5.5 - Prob. 33AYUCh. 5.5 - Prob. 34AYUCh. 5.5 - Prob. 35AYUCh. 5.5 - Prob. 36AYUCh. 5.5 - Prob. 37AYUCh. 5.5 - Prob. 38AYUCh. 5.5 - In Problems 19-54, solve each inequality...Ch. 5.5 - Prob. 40AYUCh. 5.5 - Prob. 41AYUCh. 5.5 - Prob. 42AYUCh. 5.5 - Prob. 43AYUCh. 5.5 - Prob. 44AYUCh. 5.5 - Prob. 45AYUCh. 5.5 - Prob. 46AYUCh. 5.5 - Prob. 47AYUCh. 5.5 - Prob. 48AYUCh. 5.5 - Prob. 49AYUCh. 5.5 - Prob. 50AYUCh. 5.5 - Prob. 51AYUCh. 5.5 - Prob. 52AYUCh. 5.5 - Prob. 53AYUCh. 5.5 - Prob. 54AYUCh. 5.5 - Prob. 55AYUCh. 5.5 - Prob. 56AYUCh. 5.5 - Prob. 57AYUCh. 5.5 - Prob. 58AYUCh. 5.5 - Prob. 59AYUCh. 5.5 - Prob. 60AYUCh. 5.5 - Prob. 61AYUCh. 5.5 - Prob. 62AYUCh. 5.5 - Prob. 63AYUCh. 5.5 - Prob. 64AYUCh. 5.5 - Prob. 65AYUCh. 5.5 - Prob. 66AYUCh. 5.5 - Prob. 67AYUCh. 5.5 - Prob. 68AYUCh. 5.5 - Prob. 69AYUCh. 5.5 - Prob. 70AYUCh. 5.5 - Prob. 71AYUCh. 5.5 - Prob. 72AYUCh. 5.5 - Prob. 73AYUCh. 5.5 - Prob. 74AYUCh. 5.5 - Prob. 75AYUCh. 5.5 - Prob. 76AYUCh. 5.5 - Prob. 77AYUCh. 5.5 - Prob. 78AYUCh. 5.5 - Prob. 79AYUCh. 5.5 - Prob. 80AYUCh. 5.5 - Prob. 81AYUCh. 5.5 - Prob. 82AYUCh. 5.5 - Prob. 83AYUCh. 5.5 - Prob. 84AYUCh. 5.5 - Prob. 85AYUCh. 5.5 - Prob. 86AYUCh. 5.5 - Prob. 87AYUCh. 5.5 - Prob. 88AYUCh. 5.6 - Prob. 1AYUCh. 5.6 - Prob. 2AYUCh. 5.6 - Prob. 3AYUCh. 5.6 - Prob. 4AYUCh. 5.6 - Prob. 5AYUCh. 5.6 - Prob. 6AYUCh. 5.6 - Prob. 7AYUCh. 5.6 - Prob. 8AYUCh. 5.6 - Prob. 9AYUCh. 5.6 - Prob. 10AYUCh. 5.6 - Prob. 11AYUCh. 5.6 - Prob. 12AYUCh. 5.6 - Prob. 13AYUCh. 5.6 - Prob. 14AYUCh. 5.6 - Prob. 15AYUCh. 5.6 - Prob. 16AYUCh. 5.6 - Prob. 17AYUCh. 5.6 - Prob. 18AYUCh. 5.6 - Prob. 19AYUCh. 5.6 - Prob. 20AYUCh. 5.6 - Prob. 21AYUCh. 5.6 - Prob. 22AYUCh. 5.6 - Prob. 23AYUCh. 5.6 - Prob. 24AYUCh. 5.6 - Prob. 25AYUCh. 5.6 - Prob. 26AYUCh. 5.6 - Prob. 27AYUCh. 5.6 - Prob. 28AYUCh. 5.6 - Prob. 29AYUCh. 5.6 - Prob. 30AYUCh. 5.6 - Prob. 31AYUCh. 5.6 - Prob. 32AYUCh. 5.6 - Prob. 33AYUCh. 5.6 - Prob. 34AYUCh. 5.6 - Prob. 35AYUCh. 5.6 - Prob. 36AYUCh. 5.6 - Prob. 37AYUCh. 5.6 - Prob. 38AYUCh. 5.6 - Prob. 39AYUCh. 5.6 - Prob. 40AYUCh. 5.6 - Prob. 41AYUCh. 5.6 - Prob. 42AYUCh. 5.6 - Prob. 43AYUCh. 5.6 - Prob. 44AYUCh. 5.6 - Prob. 45AYUCh. 5.6 - Prob. 46AYUCh. 5.6 - Prob. 47AYUCh. 5.6 - Prob. 48AYUCh. 5.6 - Prob. 49AYUCh. 5.6 - Prob. 50AYUCh. 5.6 - Prob. 51AYUCh. 5.6 - Prob. 52AYUCh. 5.6 - Prob. 53AYUCh. 5.6 - Prob. 54AYUCh. 5.6 - Prob. 55AYUCh. 5.6 - Prob. 56AYUCh. 5.6 - Prob. 57AYUCh. 5.6 - Prob. 58AYUCh. 5.6 - Prob. 59AYUCh. 5.6 - Prob. 60AYUCh. 5.6 - Prob. 61AYUCh. 5.6 - Prob. 62AYUCh. 5.6 - Prob. 63AYUCh. 5.6 - Prob. 64AYUCh. 5.6 - Prob. 65AYUCh. 5.6 - Prob. 66AYUCh. 5.6 - Prob. 67AYUCh. 5.6 - Prob. 68AYUCh. 5.6 - Prob. 69AYUCh. 5.6 - Prob. 70AYUCh. 5.6 - Prob. 71AYUCh. 5.6 - Prob. 72AYUCh. 5.6 - Prob. 73AYUCh. 5.6 - Prob. 74AYUCh. 5.6 - Prob. 75AYUCh. 5.6 - Prob. 76AYUCh. 5.6 - Prob. 77AYUCh. 5.6 - Prob. 78AYUCh. 5.6 - Prob. 79AYUCh. 5.6 - Prob. 80AYUCh. 5.6 - Prob. 81AYUCh. 5.6 - Prob. 82AYUCh. 5.6 - Prob. 83AYUCh. 5.6 - Prob. 84AYUCh. 5.6 - Prob. 85AYUCh. 5.6 - Prob. 86AYUCh. 5.6 - Prob. 87AYUCh. 5.6 - Prob. 88AYUCh. 5.6 - Prob. 89AYUCh. 5.6 - Prob. 90AYUCh. 5.6 - Prob. 91AYUCh. 5.6 - Prob. 92AYUCh. 5.6 - Prob. 93AYUCh. 5.6 - Prob. 94AYUCh. 5.6 - Prob. 95AYUCh. 5.6 - Prob. 96AYUCh. 5.6 - Prob. 97AYUCh. 5.6 - Prob. 98AYUCh. 5.6 - Prob. 99AYUCh. 5.6 - Prob. 100AYUCh. 5.6 - Prob. 101AYUCh. 5.6 - Prob. 102AYUCh. 5.6 - Prob. 103AYUCh. 5.6 - Prob. 104AYUCh. 5.6 - Prob. 105AYUCh. 5.6 - Prob. 106AYUCh. 5.6 - Prob. 107AYUCh. 5.6 - Prob. 108AYUCh. 5.6 - Prob. 109AYUCh. 5.6 - Prob. 110AYUCh. 5.6 - Prob. 111AYUCh. 5.6 - Prob. 112AYUCh. 5.6 - Prob. 113AYUCh. 5.6 - Prob. 114AYUCh. 5.6 - Prob. 115AYUCh. 5.6 - Prob. 116AYUCh. 5.6 - Prob. 117AYUCh. 5.6 - Prob. 118AYUCh. 5.6 - Prob. 120AYUCh. 5.6 - Prob. 121AYUCh. 5.6 - Prob. 122AYUCh. 5.6 - Prob. 123AYUCh. 5.6 - Prob. 124AYUCh. 5.6 - Prob. 125AYUCh. 5.6 - Prob. 126AYUCh. 5.6 - Prob. 127AYUCh. 5.6 - Prob. 128AYUCh. 5.6 - Prob. 129AYUCh. 5.6 - Prob. 130AYUCh. 5.6 - Prob. 131AYUCh. 5.6 - Prob. 132AYUCh. 5.6 - Prob. 133AYUCh. 5.6 - Prob. 134AYUCh. 5.6 - Prob. 135AYUCh. 5.7 - Prob. 1AYUCh. 5.7 - Prob. 2AYUCh. 5.7 - Prob. 3AYUCh. 5.7 - Prob. 4AYUCh. 5.7 - Prob. 5AYUCh. 5.7 - Prob. 6AYUCh. 5.7 - Prob. 7AYUCh. 5.7 - Prob. 8AYUCh. 5.7 - Prob. 9AYUCh. 5.7 - Prob. 10AYUCh. 5.7 - Prob. 11AYUCh. 5.7 - Prob. 12AYUCh. 5.7 - Prob. 13AYUCh. 5.7 - Prob. 14AYUCh. 5.7 - Prob. 15AYUCh. 5.7 - Prob. 16AYUCh. 5.7 - Prob. 17AYUCh. 5.7 - Prob. 18AYUCh. 5.7 - Prob. 19AYUCh. 5.7 - Prob. 20AYUCh. 5.7 - Prob. 21AYUCh. 5.7 - Prob. 22AYUCh. 5.7 - Prob. 23AYUCh. 5.7 - Prob. 24AYUCh. 5.7 - Prob. 25AYUCh. 5.7 - Prob. 26AYUCh. 5.7 - Prob. 27AYUCh. 5.7 - Prob. 28AYUCh. 5.7 - Prob. 29AYUCh. 5.7 - Prob. 30AYUCh. 5.7 - Prob. 31AYUCh. 5.7 - Prob. 32AYUCh. 5.7 - Prob. 33AYUCh. 5.7 - Prob. 34AYUCh. 5.7 - Prob. 35AYUCh. 5.7 - Prob. 36AYUCh. 5.7 - Prob. 37AYUCh. 5.7 - Prob. 38AYUCh. 5.7 - Prob. 39AYUCh. 5.7 - Prob. 40AYUCh. 5.7 - Prob. 41AYUCh. 5.7 - Prob. 42AYUCh. 5.7 - Prob. 43AYUCh. 5.7 - Prob. 44AYUCh. 5.7 - Prob. 45AYUCh. 5.7 - Prob. 46AYUCh. 5.7 - Prob. 47AYUCh. 5.7 - Prob. 48AYUCh. 5.7 - Prob. 49AYUCh. 5.7 - Prob. 50AYUCh. 5.7 - Prob. 51AYUCh. 5.7 - Prob. 52AYUCh. 5.7 - Prob. 53AYUCh. 5.7 - Prob. 54AYUCh. 5.7 - Prob. 55AYUCh. 5.7 - Prob. 56AYUCh. 5.7 - Prob. 57AYUCh. 5.7 - Prob. 58AYUCh. 5.7 - Prob. 59AYUCh. 5.7 - Prob. 60AYUCh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Prob. 39RECh. 5 - Prob. 40RECh. 5 - Prob. 41RECh. 5 - Prob. 42RECh. 5 - Prob. 43RECh. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 - Prob. 46RECh. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - Prob. 49RECh. 5 - Prob. 50RECh. 5 - Prob. 51RECh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 1CRCh. 5 - Prob. 2CRCh. 5 - Prob. 3CRCh. 5 - Prob. 4CRCh. 5 - Prob. 5CRCh. 5 - Prob. 6CRCh. 5 - Prob. 7CRCh. 5 - Prob. 8CRCh. 5 - Prob. 9CRCh. 5 - Prob. 10CRCh. 5 - Prob. 11CRCh. 5 - Prob. 12CRCh. 5 - Prob. 13CRCh. 5 - Prob. 14CRCh. 5 - Prob. 15CRCh. 5 - Prob. 16CRCh. 5 - Prob. 17CRCh. 5 - Prob. 18CRCh. 5 - Prob. 19CRCh. 5 - Prob. 20CRCh. 5 - Prob. 21CRCh. 5 - Prob. 22CRCh. 5 - Prob. 23CRCh. 5 - Prob. 24CR
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- 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]arrow_forwardR 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]arrow_forwardQuestion 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]arrow_forward
- part b pleasearrow_forwardQuestion 5 (a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the matrix a cl |df equals 3 and the determinant of determinant of the matrix a+3b cl d+3e f ГЪ e [ c ] equals 2. Compute the [5] (b) Calculate the adjugate Adj (A) of the 2 × 2 matrix [1 2 A = over R. (c) Working over the field F3 with 3 elements, use row and column operations to put the matrix [6] 0123] A = 3210 into canonical form for equivalence and write down the canonical form. What is the rank of A as a matrix over F3? 4arrow_forwardQuestion 2 In this question, V = Q4 and - U = {(x, y, z, w) EV | x+y2w+ z = 0}, W = {(x, y, z, w) € V | x − 2y + w − z = 0}, Z = {(x, y, z, w) € V | xyzw = 0}. (a) Determine which of U, W, Z are subspaces of V. Justify your answers. (b) Show that UW is a subspace of V and determine its dimension. (c) Is VU+W? Is V = UW? Justify your answers. [10] [7] '00'arrow_forward
- Tools Sign in Different masses and Indicated velocities Rotational inert > C C Chegg 39. The balls shown have different masses and speeds. Rank the following from greatest to least: 2.0 m/s 8.5 m/s 9.0 m/s 12.0 m/s 1.0 kg A 1.2 kg B 0.8 kg C 5.0 kg D C a. The momenta b. The impulses needed to stop the balls Solved 39. The balls shown have different masses and speeds. | Chegg.com Images may be subject to copyright. Learn More Share H Save Visit > quizlet.com%2FBoyE3qwOAUqXvw95Fgh5Rw.jpg&imgrefurl=https%3A%2F%2Fquizlet.com%2F529359992%2Fc. Xarrow_forwardSimplify the below expression. 3 - (-7)arrow_forward(6) ≤ a) Determine the following groups: Homz(Q, Z), Homz(Q, Q), Homz(Q/Z, Z) for n E N. Homz(Z/nZ, Q) b) Show for ME MR: HomR (R, M) = M.arrow_forward
- 1. If f(x² + 1) = x + 5x² + 3, what is f(x² - 1)?arrow_forward2. What is the total length of the shortest path that goes from (0,4) to a point on the x-axis, then to a point on the line y = 6, then to (18.4)?arrow_forwardموضوع الدرس Prove that Determine the following groups Homz(QZ) Hom = (Q13,Z) Homz(Q), Hom/z/nZ, Qt for neN- (2) Every factor group of adivisible group is divisble. • If R is a Skew ficald (aring with identity and each non Zero element is invertible then every R-module is free.arrow_forward
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