EBK ALGEBRA FOUNDATIONS
15th Edition
ISBN: 9780321978929
Author: Martin-Gay
Publisher: PEARSON
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Chapter 3.2, Problem 37ES
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To find: The solution of equation.
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Într-un bloc sunt apartamente cu 2 camere și apartamente cu 3 camere , în total 20 de apartamente și 45 de camere.Calculați câte apartamente sunt cu 2 camere și câte apartamente sunt cu 3 camere.
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]
Chapter 3 Solutions
EBK ALGEBRA FOUNDATIONS
Ch. 3.1 - Use the choices below to fill in each blank. Some...Ch. 3.1 - Prob. 2VRVCCh. 3.1 - Prob. 3VRVCCh. 3.1 - Prob. 4VRVCCh. 3.1 - Prob. 5VRVCCh. 3.1 - Prob. 6VRVCCh. 3.1 - Prob. 7VRVCCh. 3.1 - Prob. 8VRVCCh. 3.1 - Prob. 9VRVCCh. 3.1 - Prob. 1ES
Ch. 3.1 - Prob. 2ESCh. 3.1 - Prob. 3ESCh. 3.1 - Prob. 4ESCh. 3.1 - Prob. 5ESCh. 3.1 - Prob. 6ESCh. 3.1 - Prob. 7ESCh. 3.1 - Prob. 8ESCh. 3.1 - Prob. 9ESCh. 3.1 - Prob. 10ESCh. 3.1 - Prob. 11ESCh. 3.1 - Prob. 12ESCh. 3.1 - Prob. 13ESCh. 3.1 - Prob. 14ESCh. 3.1 - Prob. 15ESCh. 3.1 - Prob. 16ESCh. 3.1 - Prob. 17ESCh. 3.1 - Prob. 18ESCh. 3.1 - Prob. 19ESCh. 3.1 - Prob. 20ESCh. 3.1 - Prob. 21ESCh. 3.1 - Prob. 22ESCh. 3.1 - Prob. 23ESCh. 3.1 - Prob. 24ESCh. 3.1 - Prob. 25ESCh. 3.1 - Prob. 26ESCh. 3.1 - Prob. 27ESCh. 3.1 - Prob. 28ESCh. 3.1 - Prob. 29ESCh. 3.1 - Prob. 30ESCh. 3.1 - Prob. 31ESCh. 3.1 - Prob. 32ESCh. 3.1 - Prob. 33ESCh. 3.1 - Prob. 34ESCh. 3.1 - Prob. 35ESCh. 3.1 - Prob. 36ESCh. 3.1 - Prob. 37ESCh. 3.1 - Prob. 38ESCh. 3.1 - Prob. 39ESCh. 3.1 - Prob. 40ESCh. 3.1 - Prob. 41ESCh. 3.1 - Prob. 42ESCh. 3.1 - Prob. 43ESCh. 3.1 - Prob. 44ESCh. 3.1 - Prob. 45ESCh. 3.1 - Prob. 46ESCh. 3.1 - Prob. 47ESCh. 3.1 - Prob. 48ESCh. 3.1 - Prob. 49ESCh. 3.1 - Prob. 50ESCh. 3.1 - Prob. 51ESCh. 3.1 - Prob. 52ESCh. 3.1 - Prob. 53ESCh. 3.1 - Prob. 54ESCh. 3.1 - Prob. 55ESCh. 3.1 - Prob. 56ESCh. 3.1 - Prob. 57ESCh. 3.1 - Prob. 58ESCh. 3.1 - Prob. 59ESCh. 3.1 - Prob. 60ESCh. 3.1 - Prob. 61ESCh. 3.1 - Prob. 62ESCh. 3.1 - Prob. 63ESCh. 3.1 - Prob. 64ESCh. 3.1 - Prob. 65ESCh. 3.1 - Prob. 66ESCh. 3.1 - Prob. 67ESCh. 3.1 - Prob. 68ESCh. 3.1 - Prob. 69ESCh. 3.1 - Prob. 70ESCh. 3.1 - Prob. 71ESCh. 3.1 - Prob. 72ESCh. 3.1 - Prob. 73ESCh. 3.1 - Prob. 74ESCh. 3.1 - Prob. 75ESCh. 3.1 - Prob. 76ESCh. 3.1 - Prob. 77ESCh. 3.1 - Prob. 78ESCh. 3.1 - Prob. 79ESCh. 3.1 - Prob. 80ESCh. 3.1 - Prob. 81ESCh. 3.1 - Prob. 82ESCh. 3.1 - Prob. 83ESCh. 3.1 - Prob. 84ESCh. 3.1 - Prob. 85ESCh. 3.1 - Prob. 86ESCh. 3.1 - Prob. 87ESCh. 3.1 - Prob. 88ESCh. 3.1 - Prob. 89ESCh. 3.1 - Prob. 90ESCh. 3.1 - Prob. 91ESCh. 3.1 - Prob. 92ESCh. 3.1 - Prob. 93ESCh. 3.1 - Prob. 94ESCh. 3.1 - Prob. 95ESCh. 3.1 - Prob. 96ESCh. 3.1 - Prob. 97ESCh. 3.1 - Prob. 98ESCh. 3.1 - Prob. 99ESCh. 3.1 - Prob. 100ESCh. 3.1 - Prob. 101ESCh. 3.1 - Prob. 102ESCh. 3.1 - Prob. 103ESCh. 3.1 - Prob. 104ESCh. 3.1 - Prob. 105ESCh. 3.1 - Prob. 106ESCh. 3.1 - Prob. 107ESCh. 3.1 - Prob. 108ESCh. 3.1 - Prob. 109ESCh. 3.1 - Prob. 110ESCh. 3.1 - Prob. 111ESCh. 3.1 - Prob. 112ESCh. 3.1 - Prob. 113ESCh. 3.1 - Prob. 114ESCh. 3.2 - Prob. 1VRVCCh. 3.2 - Prob. 2VRVCCh. 3.2 - Prob. 3VRVCCh. 3.2 - Prob. 4VRVCCh. 3.2 - Prob. 5VRVCCh. 3.2 - Prob. 6VRVCCh. 3.2 - Prob. 1ESCh. 3.2 - Prob. 2ESCh. 3.2 - Prob. 3ESCh. 3.2 - Prob. 4ESCh. 3.2 - Prob. 5ESCh. 3.2 - Prob. 6ESCh. 3.2 - Prob. 7ESCh. 3.2 - Prob. 8ESCh. 3.2 - Prob. 9ESCh. 3.2 - Prob. 10ESCh. 3.2 - Prob. 11ESCh. 3.2 - Prob. 12ESCh. 3.2 - Prob. 13ESCh. 3.2 - Prob. 14ESCh. 3.2 - Prob. 15ESCh. 3.2 - Prob. 16ESCh. 3.2 - Prob. 17ESCh. 3.2 - Prob. 18ESCh. 3.2 - Prob. 19ESCh. 3.2 - Prob. 20ESCh. 3.2 - Prob. 21ESCh. 3.2 - Prob. 22ESCh. 3.2 - Prob. 23ESCh. 3.2 - Prob. 24ESCh. 3.2 - Prob. 25ESCh. 3.2 - Prob. 26ESCh. 3.2 - Prob. 27ESCh. 3.2 - Prob. 28ESCh. 3.2 - Prob. 29ESCh. 3.2 - Prob. 30ESCh. 3.2 - Prob. 31ESCh. 3.2 - Prob. 32ESCh. 3.2 - Prob. 33ESCh. 3.2 - Prob. 34ESCh. 3.2 - Prob. 35ESCh. 3.2 - Prob. 36ESCh. 3.2 - Prob. 37ESCh. 3.2 - Prob. 38ESCh. 3.2 - Prob. 39ESCh. 3.2 - Prob. 40ESCh. 3.2 - Prob. 41ESCh. 3.2 - Prob. 42ESCh. 3.2 - Prob. 43ESCh. 3.2 - Prob. 44ESCh. 3.2 - Prob. 45ESCh. 3.2 - Prob. 46ESCh. 3.2 - Prob. 47ESCh. 3.2 - Prob. 48ESCh. 3.2 - Prob. 49ESCh. 3.2 - Prob. 50ESCh. 3.2 - Prob. 51ESCh. 3.2 - Prob. 52ESCh. 3.2 - Prob. 53ESCh. 3.2 - Prob. 54ESCh. 3.2 - Prob. 55ESCh. 3.2 - Prob. 56ESCh. 3.2 - Prob. 57ESCh. 3.2 - Prob. 58ESCh. 3.2 - Prob. 59ESCh. 3.2 - Prob. 60ESCh. 3.2 - Prob. 61ESCh. 3.2 - Prob. 62ESCh. 3.2 - Prob. 63ESCh. 3.2 - Prob. 64ESCh. 3.2 - Prob. 65ESCh. 3.2 - Prob. 66ESCh. 3.2 - Prob. 67ESCh. 3.2 - Prob. 68ESCh. 3.2 - Prob. 69ESCh. 3.2 - Prob. 70ESCh. 3.2 - Prob. 71ESCh. 3.2 - Prob. 72ESCh. 3.2 - Prob. 73ESCh. 3.2 - Prob. 74ESCh. 3.2 - Prob. 75ESCh. 3.2 - Prob. 76ESCh. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Prob. 78ESCh. 3.2 - Prob. 79ESCh. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Prob. 82ESCh. 3.2 - Prob. 83ESCh. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Prob. 85ESCh. 3.2 - Objective Translating Write each phrase asa...Ch. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Prob. 90ESCh. 3.2 - Prob. 91ESCh. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Objective Translating Write each phrase as a...Ch. 3.2 - Prob. 95ESCh. 3.2 - Prob. 96ESCh. 3.2 - Prob. 97ESCh. 3.2 - Prob. 98ESCh. 3.2 - Prob. 99ESCh. 3.2 - Prob. 100ESCh. 3.2 - Prob. 101ESCh. 3.2 - Prob. 102ESCh. 3.2 - Prob. 103ESCh. 3.2 - Prob. 104ESCh. 3.2 - Prob. 105ESCh. 3.2 - Prob. 106ESCh. 3.2 - Prob. 107ESCh. 3.2 - Prob. 108ESCh. 3.2 - Prob. 109ESCh. 3.2 - Prob. 110ESCh. 3.3 - Prob. 1VRVCCh. 3.3 - Prob. 2VRVCCh. 3.3 - Prob. 3VRVCCh. 3.3 - Prob. 4VRVCCh. 3.3 - Prob. 5VRVCCh. 3.3 - Prob. 6VRVCCh. 3.3 - Prob. 1ESCh. 3.3 - Prob. 2ESCh. 3.3 - Prob. 3ESCh. 3.3 - Prob. 4ESCh. 3.3 - Prob. 5ESCh. 3.3 - Prob. 6ESCh. 3.3 - Prob. 7ESCh. 3.3 - Prob. 8ESCh. 3.3 - Prob. 9ESCh. 3.3 - Prob. 10ESCh. 3.3 - Prob. 11ESCh. 3.3 - Prob. 12ESCh. 3.3 - Prob. 13ESCh. 3.3 - Prob. 14ESCh. 3.3 - Prob. 15ESCh. 3.3 - Prob. 16ESCh. 3.3 - Prob. 17ESCh. 3.3 - Prob. 18ESCh. 3.3 - Prob. 19ESCh. 3.3 - Prob. 20ESCh. 3.3 - Prob. 21ESCh. 3.3 - Prob. 22ESCh. 3.3 - Prob. 23ESCh. 3.3 - Prob. 24ESCh. 3.3 - Prob. 25ESCh. 3.3 - Prob. 26ESCh. 3.3 - Prob. 27ESCh. 3.3 - Prob. 28ESCh. 3.3 - Prob. 29ESCh. 3.3 - Prob. 30ESCh. 3.3 - Prob. 31ESCh. 3.3 - Prob. 32ESCh. 3.3 - Prob. 33ESCh. 3.3 - Prob. 34ESCh. 3.3 - Prob. 35ESCh. 3.3 - Prob. 36ESCh. 3.3 - Prob. 37ESCh. 3.3 - Prob. 38ESCh. 3.3 - Prob. 39ESCh. 3.3 - Prob. 40ESCh. 3.3 - Prob. 41ESCh. 3.3 - Prob. 42ESCh. 3.3 - Prob. 43ESCh. 3.3 - Prob. 44ESCh. 3.3 - Prob. 45ESCh. 3.3 - Prob. 46ESCh. 3.3 - Prob. 47ESCh. 3.3 - Prob. 48ESCh. 3.3 - Prob. 49ESCh. 3.3 - Prob. 50ESCh. 3.3 - Prob. 51ESCh. 3.3 - Prob. 52ESCh. 3.3 - Prob. 53ESCh. 3.3 - Prob. 54ESCh. 3.3 - Prob. 55ESCh. 3.3 - Prob. 56ESCh. 3.3 - Prob. 57ESCh. 3.3 - Prob. 58ESCh. 3.3 - Prob. 59ESCh. 3.3 - Prob. 60ESCh. 3.3 - Prob. 61ESCh. 3.3 - Prob. 62ESCh. 3.3 - Prob. 63ESCh. 3.3 - Prob. 64ESCh. 3.3 - Prob. 65ESCh. 3.3 - Prob. 66ESCh. 3.3 - Prob. 67ESCh. 3.3 - Prob. 68ESCh. 3.3 - Prob. 69ESCh. 3.3 - Prob. 70ESCh. 3.3 - Prob. 71ESCh. 3.3 - Prob. 72ESCh. 3.3 - Prob. 73ESCh. 3.3 - Prob. 74ESCh. 3.3 - Prob. 75ESCh. 3.3 - The following bar graph shows the number of U.S....Ch. 3.3 - Prob. 77ESCh. 3.3 - Prob. 78ESCh. 3.3 - Prob. 79ESCh. 3.3 - Prob. 80ESCh. 3.3 - Prob. 81ESCh. 3.3 - Using the Steps for Solving an Equation, choose...Ch. 3.3 - Prob. 83ESCh. 3.3 - Prob. 84ESCh. 3.3 - Prob. 85ESCh. 3.3 - Prob. 86ESCh. 3.3 - Prob. 87ESCh. 3.3 - Prob. 88ESCh. 3.3 - Prob. 89ESCh. 3.3 - Prob. 90ESCh. 3.3 - Prob. 91ESCh. 3.3 - Prob. 92ESCh. 3.4 - Prob. 1ESCh. 3.4 - Prob. 2ESCh. 3.4 - Prob. 3ESCh. 3.4 - Prob. 4ESCh. 3.4 - Prob. 5ESCh. 3.4 - Prob. 6ESCh. 3.4 - Prob. 7ESCh. 3.4 - Prob. 8ESCh. 3.4 - Prob. 9ESCh. 3.4 - Prob. 10ESCh. 3.4 - Prob. 11ESCh. 3.4 - Prob. 12ESCh. 3.4 - Prob. 13ESCh. 3.4 - Prob. 14ESCh. 3.4 - Prob. 15ESCh. 3.4 - Prob. 16ESCh. 3.4 - Prob. 17ESCh. 3.4 - Prob. 18ESCh. 3.4 - Prob. 19ESCh. 3.4 - Prob. 20ESCh. 3.4 - Prob. 21ESCh. 3.4 - Prob. 22ESCh. 3.4 - Prob. 23ESCh. 3.4 - Prob. 24ESCh. 3.4 - Prob. 25ESCh. 3.4 - Prob. 26ESCh. 3.4 - Prob. 27ESCh. 3.4 - Prob. 28ESCh. 3.4 - Prob. 29ESCh. 3.4 - Prob. 30ESCh. 3.4 - Prob. 31ESCh. 3.4 - Prob. 32ESCh. 3.4 - Prob. 33ESCh. 3.4 - Prob. 34ESCh. 3.4 - Prob. 35ESCh. 3.4 - Prob. 36ESCh. 3.4 - Prob. 37ESCh. 3.4 - Prob. 38ESCh. 3.4 - Prob. 39ESCh. 3.4 - California contains the largest state population...Ch. 3.4 - Prob. 41ESCh. 3.4 - Prob. 42ESCh. 3.4 - Prob. 43ESCh. 3.4 - Prob. 44ESCh. 3.4 - Prob. 45ESCh. 3.4 - Prob. 46ESCh. 3.4 - Prob. 47ESCh. 3.4 - Prob. 48ESCh. 3.4 - Prob. 49ESCh. 3.4 - Prob. 50ESCh. 3.4 - Prob. 51ESCh. 3.4 - Prob. 52ESCh. 3.4 - Prob. 53ESCh. 3.4 - Prob. 54ESCh. 3.4 - Prob. 55ESCh. 3.4 - Prob. 56ESCh. 3.4 - Prob. 57ESCh. 3.4 - Prob. 58ESCh. 3.4 - Prob. 59ESCh. 3.4 - Prob. 60ESCh. 3 - For the table below, identify each as an...Ch. 3 - Prob. 2IRCh. 3 - Prob. 3IRCh. 3 - Prob. 4IRCh. 3 - Prob. 5IRCh. 3 - Prob. 6IRCh. 3 - Prob. 7IRCh. 3 - Prob. 8IRCh. 3 - Prob. 9IRCh. 3 - Prob. 10IRCh. 3 - Prob. 11IRCh. 3 - Prob. 12IRCh. 3 - Prob. 13IRCh. 3 - Prob. 14IRCh. 3 - Prob. 15IRCh. 3 - Prob. 16IRCh. 3 - Prob. 17IRCh. 3 - Prob. 18IRCh. 3 - Prob. 19IRCh. 3 - Prob. 20IRCh. 3 - Prob. 21IRCh. 3 - Prob. 22IRCh. 3 - Prob. 23IRCh. 3 - Prob. 24IRCh. 3 - Prob. 25IRCh. 3 - Prob. 26IRCh. 3 - Prob. 27IRCh. 3 - Prob. 28IRCh. 3 - Prob. 29IRCh. 3 - Prob. 30IRCh. 3 - Prob. 31IRCh. 3 - Prob. 32IRCh. 3 - Prob. 33IRCh. 3 - Prob. 34IRCh. 3 - Translating Write each phrase as an algebraic...Ch. 3 - Translating Write each phrase as an algebraic...Ch. 3 - Prob. 37IRCh. 3 - Translating Write each phrase as an algebraic...Ch. 3 - Prob. 39IRCh. 3 - Translating Write each phrase as an algebraic...Ch. 3 - Prob. 1VCCh. 3 - Prob. 2VCCh. 3 - Prob. 3VCCh. 3 - Prob. 4VCCh. 3 - Fill in each blank with one of the words or...Ch. 3 - Prob. 6VCCh. 3 - Prob. 7VCCh. 3 - Prob. 8VCCh. 3 - Prob. 9VCCh. 3 - Prob. 10VCCh. 3 - Prob. 11VCCh. 3 - Prob. 12VCCh. 3 - Prob. 13VCCh. 3 - Prob. 1RCh. 3 - Prob. 2RCh. 3 - Prob. 3RCh. 3 - Prob. 4RCh. 3 - Prob. 5RCh. 3 - Prob. 6RCh. 3 - Prob. 7RCh. 3 - Prob. 8RCh. 3 - Prob. 9RCh. 3 - Prob. 10RCh. 3 - Prob. 11RCh. 3 - Prob. 12RCh. 3 - Prob. 13RCh. 3 - Prob. 14RCh. 3 - Prob. 15RCh. 3 - Prob. 16RCh. 3 - Prob. 17RCh. 3 - Prob. 18RCh. 3 - Prob. 19RCh. 3 - Prob. 20RCh. 3 - Prob. 21RCh. 3 - Prob. 22RCh. 3 - Prob. 23RCh. 3 - Prob. 24RCh. 3 - Prob. 25RCh. 3 - Prob. 26RCh. 3 - Prob. 27RCh. 3 - Prob. 28RCh. 3 - Prob. 29RCh. 3 - Prob. 30RCh. 3 - Prob. 31RCh. 3 - Prob. 32RCh. 3 - Prob. 33RCh. 3 - Prob. 34RCh. 3 - Prob. 35RCh. 3 - Prob. 36RCh. 3 - Prob. 37RCh. 3 - Prob. 38RCh. 3 - Prob. 39RCh. 3 - Prob. 40RCh. 3 - Prob. 41RCh. 3 - Prob. 42RCh. 3 - Prob. 43RCh. 3 - Prob. 44RCh. 3 - Prob. 45RCh. 3 - Prob. 46RCh. 3 - Prob. 47RCh. 3 - Prob. 48RCh. 3 - Prob. 49RCh. 3 - Prob. 50RCh. 3 - Prob. 51RCh. 3 - Prob. 52RCh. 3 - Prob. 53RCh. 3 - Prob. 54RCh. 3 - Prob. 55RCh. 3 - Prob. 56RCh. 3 - Prob. 57RCh. 3 - Prob. 58RCh. 3 - Prob. 59RCh. 3 - Prob. 60RCh. 3 - Prob. 61RCh. 3 - Prob. 62RCh. 3 - Prob. 63RCh. 3 - Prob. 64RCh. 3 - Prob. 65RCh. 3 - Prob. 66RCh. 3 - Prob. 67RCh. 3 - Prob. 68RCh. 3 - Prob. 69RCh. 3 - Prob. 70RCh. 3 - Prob. 71RCh. 3 - Prob. 72RCh. 3 - Prob. 73RCh. 3 - Prob. 74RCh. 3 - Prob. 75RCh. 3 - Prob. 76RCh. 3 - Prob. 77RCh. 3 - Prob. 78RCh. 3 - Prob. 79RCh. 3 - Prob. 80RCh. 3 - Prob. 81RCh. 3 - Prob. 82RCh. 3 - Prob. 83RCh. 3 - Prob. 84RCh. 3 - Prob. 85RCh. 3 - Prob. 86RCh. 3 - Prob. 87RCh. 3 - Prob. 88RCh. 3 - Prob. 89RCh. 3 - Prob. 90RCh. 3 - Prob. 91RCh. 3 - Prob. 92RCh. 3 - Prob. 93RCh. 3 - Prob. 94RCh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Prob. 10TCh. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - Prob. 15TCh. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CRCh. 3 - Prob. 10CRCh. 3 - Prob. 11CRCh. 3 - Prob. 12CRCh. 3 - Prob. 13CRCh. 3 - Prob. 14CRCh. 3 - Prob. 15CRCh. 3 - Prob. 16CRCh. 3 - Prob. 17CRCh. 3 - Prob. 18CRCh. 3 - Prob. 19CRCh. 3 - Prob. 20CRCh. 3 - Prob. 21CRCh. 3 - Prob. 22CRCh. 3 - Prob. 23CRCh. 3 - Prob. 24CRCh. 3 - Prob. 25CRCh. 3 - Prob. 26CRCh. 3 - Prob. 27CRCh. 3 - Prob. 28CRCh. 3 - Prob. 29CRCh. 3 - Prob. 30CRCh. 3 - Prob. 31CRCh. 3 - Prob. 32CRCh. 3 - Prob. 33CRCh. 3 - Prob. 34CRCh. 3 - Prob. 35CRCh. 3 - Prob. 36CRCh. 3 - Prob. 37CRCh. 3 - Prob. 38CRCh. 3 - Prob. 39CRCh. 3 - Prob. 40CRCh. 3 - Prob. 41CRCh. 3 - Prob. 42CRCh. 3 - Prob. 43CRCh. 3 - Prob. 44CRCh. 3 - Prob. 45CRCh. 3 - Prob. 46CRCh. 3 - Prob. 47CRCh. 3 - Prob. 48CRCh. 3 - Prob. 49CRCh. 3 - Prob. 50CR
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- 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]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_forwardpart b pleasearrow_forward
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