EBK ALGEBRA FOUNDATIONS
15th Edition
ISBN: 9780321978929
Author: Martin-Gay
Publisher: PEARSON
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Chapter 16.2, Problem 3VRVC
To determine
Tomatch: the absolute value of the given equation with equivalent equations in option.
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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 16 Solutions
EBK ALGEBRA FOUNDATIONS
Ch. 16.1 - Use the choices below to fill in each blank. Or ...Ch. 16.1 - Use the choices below to fill in each blank. Or ...Ch. 16.1 - Prob. 3VRVCCh. 16.1 - Prob. 4VRVCCh. 16.1 - Prob. 5VRVCCh. 16.1 - Prob. 6VRVCCh. 16.1 - Prob. 1ESCh. 16.1 - Prob. 2ESCh. 16.1 - Prob. 3ESCh. 16.1 - Prob. 4ES
Ch. 16.1 - Prob. 5ESCh. 16.1 - Prob. 6ESCh. 16.1 - Prob. 7ESCh. 16.1 - Prob. 8ESCh. 16.1 - Prob. 9ESCh. 16.1 - Prob. 10ESCh. 16.1 - Prob. 11ESCh. 16.1 - Prob. 12ESCh. 16.1 - Prob. 13ESCh. 16.1 - Prob. 14ESCh. 16.1 - Prob. 15ESCh. 16.1 - Prob. 16ESCh. 16.1 - Prob. 17ESCh. 16.1 - Prob. 18ESCh. 16.1 - Prob. 19ESCh. 16.1 - Prob. 20ESCh. 16.1 - Prob. 21ESCh. 16.1 - Prob. 22ESCh. 16.1 - Prob. 23ESCh. 16.1 - Solve each compound inequality. Write solutions in...Ch. 16.1 - Prob. 25ESCh. 16.1 - Prob. 26ESCh. 16.1 - Prob. 27ESCh. 16.1 - Prob. 28ESCh. 16.1 - Prob. 29ESCh. 16.1 - Prob. 30ESCh. 16.1 - Prob. 31ESCh. 16.1 - Prob. 32ESCh. 16.1 - Prob. 33ESCh. 16.1 - Prob. 34ESCh. 16.1 - Prob. 35ESCh. 16.1 - Prob. 36ESCh. 16.1 - Prob. 37ESCh. 16.1 - Prob. 38ESCh. 16.1 - Prob. 39ESCh. 16.1 - Prob. 40ESCh. 16.1 - Prob. 41ESCh. 16.1 - Prob. 42ESCh. 16.1 - Prob. 43ESCh. 16.1 - Prob. 44ESCh. 16.1 - Prob. 45ESCh. 16.1 - Prob. 46ESCh. 16.1 - Prob. 47ESCh. 16.1 - Objectives B D Mixed Practice Solve each compound...Ch. 16.1 - Prob. 49ESCh. 16.1 - Prob. 50ESCh. 16.1 - Prob. 51ESCh. 16.1 - Prob. 52ESCh. 16.1 - Prob. 53ESCh. 16.1 - Prob. 54ESCh. 16.1 - Prob. 55ESCh. 16.1 - Prob. 56ESCh. 16.1 - Prob. 57ESCh. 16.1 - Prob. 58ESCh. 16.1 - Prob. 59ESCh. 16.1 - Prob. 60ESCh. 16.1 - Prob. 61ESCh. 16.1 - Prob. 62ESCh. 16.1 - Prob. 63ESCh. 16.1 - Prob. 64ESCh. 16.1 - Prob. 65ESCh. 16.1 - Prob. 66ESCh. 16.1 - Prob. 67ESCh. 16.1 - Prob. 68ESCh. 16.1 - Prob. 69ESCh. 16.1 - Prob. 70ESCh. 16.1 - Prob. 71ESCh. 16.1 - Prob. 72ESCh. 16.1 - Prob. 73ESCh. 16.1 - Prob. 74ESCh. 16.1 - Prob. 75ESCh. 16.1 - Prob. 76ESCh. 16.1 - Prob. 77ESCh. 16.1 - Prob. 78ESCh. 16.1 - Prob. 79ESCh. 16.1 - Prob. 80ESCh. 16.1 - Prob. 81ESCh. 16.1 - Prob. 82ESCh. 16.1 - Prob. 83ESCh. 16.1 - Prob. 84ESCh. 16.1 - Prob. 85ESCh. 16.1 - Prob. 86ESCh. 16.1 - Prob. 87ESCh. 16.1 - Prob. 88ESCh. 16.1 - Prob. 89ESCh. 16.1 - Prob. 90ESCh. 16.1 - Prob. 91ESCh. 16.1 - Prob. 92ESCh. 16.1 - Prob. 93ESCh. 16.1 - Prob. 94ESCh. 16.2 - Match each absolute value equation with the...Ch. 16.2 - Prob. 2VRVCCh. 16.2 - Prob. 3VRVCCh. 16.2 - Prob. 4VRVCCh. 16.2 - Prob. 5VRVCCh. 16.2 - Prob. 1ESCh. 16.2 - Prob. 2ESCh. 16.2 - Prob. 3ESCh. 16.2 - Prob. 4ESCh. 16.2 - Prob. 5ESCh. 16.2 - Prob. 6ESCh. 16.2 - Prob. 7ESCh. 16.2 - Prob. 8ESCh. 16.2 - Objective A Solve each absolute value equation....Ch. 16.2 - Prob. 10ESCh. 16.2 - Prob. 11ESCh. 16.2 - Prob. 12ESCh. 16.2 - Prob. 13ESCh. 16.2 - Prob. 14ESCh. 16.2 - Prob. 15ESCh. 16.2 - Prob. 16ESCh. 16.2 - Prob. 17ESCh. 16.2 - Prob. 18ESCh. 16.2 - Prob. 19ESCh. 16.2 - Prob. 20ESCh. 16.2 - Prob. 21ESCh. 16.2 - Prob. 22ESCh. 16.2 - Prob. 23ESCh. 16.2 - Prob. 24ESCh. 16.2 - Mixed Practice Solve each absolute value equation....Ch. 16.2 - Prob. 26ESCh. 16.2 - Prob. 27ESCh. 16.2 - Prob. 28ESCh. 16.2 - Prob. 29ESCh. 16.2 - Prob. 30ESCh. 16.2 - Prob. 31ESCh. 16.2 - Prob. 32ESCh. 16.2 - Prob. 33ESCh. 16.2 - Prob. 34ESCh. 16.2 - Prob. 35ESCh. 16.2 - Prob. 36ESCh. 16.2 - Prob. 37ESCh. 16.2 - Prob. 38ESCh. 16.2 - Prob. 39ESCh. 16.2 - Prob. 40ESCh. 16.2 - Prob. 41ESCh. 16.2 - Prob. 42ESCh. 16.2 - Prob. 43ESCh. 16.2 - Prob. 44ESCh. 16.2 - Prob. 45ESCh. 16.2 - Prob. 46ESCh. 16.2 - Prob. 47ESCh. 16.2 - Prob. 48ESCh. 16.2 - Prob. 49ESCh. 16.2 - Prob. 50ESCh. 16.2 - Prob. 51ESCh. 16.2 - Prob. 52ESCh. 16.2 - Prob. 53ESCh. 16.2 - Prob. 54ESCh. 16.2 - Prob. 55ESCh. 16.2 - Prob. 56ESCh. 16.2 - Prob. 57ESCh. 16.2 - Prob. 58ESCh. 16.2 - Prob. 59ESCh. 16.2 - Prob. 60ESCh. 16.2 - Prob. 61ESCh. 16.2 - Prob. 62ESCh. 16.2 - Prob. 63ESCh. 16.2 - Prob. 64ESCh. 16.2 - Prob. 65ESCh. 16.2 - Prob. 66ESCh. 16.2 - Prob. 67ESCh. 16.2 - Prob. 68ESCh. 16.2 - Prob. 69ESCh. 16.2 - Prob. 70ESCh. 16.2 - Prob. 71ESCh. 16.2 - Prob. 72ESCh. 16.2 - Prob. 73ESCh. 16.2 - Prob. 74ESCh. 16.2 - Prob. 75ESCh. 16.2 - Prob. 76ESCh. 16.2 - Prob. 77ESCh. 16.2 - Prob. 78ESCh. 16.2 - Prob. 79ESCh. 16.2 - Prob. 80ESCh. 16.2 - Prob. 81ESCh. 16.2 - Prob. 82ESCh. 16.2 - Prob. 83ESCh. 16.2 - Prob. 84ESCh. 16.2 - Prob. 85ESCh. 16.2 - Prob. 86ESCh. 16.2 - Prob. 87ESCh. 16.2 - Prob. 88ESCh. 16.2 - Prob. 89ESCh. 16.2 - Prob. 90ESCh. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Prob. 1ESCh. 16.3 - Prob. 2ESCh. 16.3 - Prob. 3ESCh. 16.3 - Prob. 4ESCh. 16.3 - Prob. 5ESCh. 16.3 - Prob. 6ESCh. 16.3 - Prob. 7ESCh. 16.3 - Objective A Solve each ineqaulity. Then graph the...Ch. 16.3 - Prob. 9ESCh. 16.3 - Prob. 10ESCh. 16.3 - Prob. 11ESCh. 16.3 - Prob. 12ESCh. 16.3 - Prob. 13ESCh. 16.3 - Prob. 14ESCh. 16.3 - Prob. 15ESCh. 16.3 - Prob. 16ESCh. 16.3 - Prob. 17ESCh. 16.3 - Prob. 18ESCh. 16.3 - Prob. 19ESCh. 16.3 - Prob. 20ESCh. 16.3 - Objective B Solve each ineqaulity. Graph the...Ch. 16.3 - Prob. 22ESCh. 16.3 - Prob. 23ESCh. 16.3 - Prob. 24ESCh. 16.3 - Prob. 25ESCh. 16.3 - Prob. 26ESCh. 16.3 - Prob. 27ESCh. 16.3 - Prob. 28ESCh. 16.3 - Prob. 29ESCh. 16.3 - Prob. 30ESCh. 16.3 - Prob. 31ESCh. 16.3 - Prob. 32ESCh. 16.3 - Prob. 33ESCh. 16.3 - Prob. 34ESCh. 16.3 - Prob. 35ESCh. 16.3 - Prob. 36ESCh. 16.3 - Prob. 37ESCh. 16.3 - Prob. 38ESCh. 16.3 - Prob. 39ESCh. 16.3 - Prob. 40ESCh. 16.3 - Prob. 41ESCh. 16.3 - Prob. 42ESCh. 16.3 - Prob. 43ESCh. 16.3 - Prob. 44ESCh. 16.3 - Prob. 45ESCh. 16.3 - Prob. 46ESCh. 16.3 - Prob. 47ESCh. 16.3 - Prob. 48ESCh. 16.3 - Prob. 49ESCh. 16.3 - Prob. 50ESCh. 16.3 - Prob. 51ESCh. 16.3 - Prob. 52ESCh. 16.3 - Prob. 53ESCh. 16.3 - Prob. 54ESCh. 16.3 - Prob. 55ESCh. 16.3 - Prob. 56ESCh. 16.3 - Prob. 57ESCh. 16.3 - Prob. 58ESCh. 16.3 - Prob. 59ESCh. 16.3 - Prob. 60ESCh. 16.3 - Prob. 61ESCh. 16.3 - Prob. 62ESCh. 16.3 - Prob. 63ESCh. 16.3 - Prob. 64ESCh. 16.3 - Prob. 65ESCh. 16.3 - Prob. 66ESCh. 16.3 - Prob. 67ESCh. 16.3 - Prob. 68ESCh. 16.3 - Prob. 69ESCh. 16.3 - Prob. 70ESCh. 16.3 - Prob. 71ESCh. 16.3 - Prob. 72ESCh. 16.3 - Prob. 73ESCh. 16.3 - Prob. 74ESCh. 16.3 - Prob. 75ESCh. 16.3 - Prob. 76ESCh. 16.3 - Prob. 77ESCh. 16.3 - Prob. 78ESCh. 16.3 - Prob. 79ESCh. 16.3 - Prob. 80ESCh. 16.3 - Prob. 81ESCh. 16.3 - Prob. 82ESCh. 16.3 - Prob. 83ESCh. 16.3 - Prob. 84ESCh. 16.3 - Prob. 85ESCh. 16.3 - Prob. 86ESCh. 16.3 - Prob. 87ESCh. 16.3 - Prob. 88ESCh. 16.3 - Prob. 89ESCh. 16.3 - Prob. 90ESCh. 16.3 - Prob. 91ESCh. 16.3 - Prob. 92ESCh. 16.3 - Prob. 93ESCh. 16.3 - Prob. 94ESCh. 16.3 - Prob. 95ESCh. 16.3 - Prob. 96ESCh. 16.4 - Prob. 1VRVCCh. 16.4 - Prob. 2VRVCCh. 16.4 - Prob. 3VRVCCh. 16.4 - Prob. 4VRVCCh. 16.4 - Prob. 5VRVCCh. 16.4 - Prob. 6VRVCCh. 16.4 - Prob. 7VRVCCh. 16.4 - Prob. 8VRVCCh. 16.4 - Prob. 9VRVCCh. 16.4 - Prob. 10VRVCCh. 16.4 - Prob. 1ESCh. 16.4 - Prob. 2ESCh. 16.4 - Prob. 3ESCh. 16.4 - Prob. 4ESCh. 16.4 - Prob. 5ESCh. 16.4 - Prob. 6ESCh. 16.4 - Prob. 7ESCh. 16.4 - Prob. 8ESCh. 16.4 - Prob. 9ESCh. 16.4 - Prob. 10ESCh. 16.4 - Prob. 11ESCh. 16.4 - Prob. 12ESCh. 16.4 - Prob. 13ESCh. 16.4 - Prob. 14ESCh. 16.4 - Prob. 15ESCh. 16.4 - Prob. 16ESCh. 16.4 - Prob. 17ESCh. 16.4 - Prob. 18ESCh. 16.4 - Prob. 19ESCh. 16.4 - Prob. 20ESCh. 16.4 - Prob. 21ESCh. 16.4 - Prob. 22ESCh. 16.4 - Prob. 23ESCh. 16.4 - Prob. 24ESCh. 16.4 - Prob. 25ESCh. 16.4 - Prob. 26ESCh. 16.4 - Prob. 27ESCh. 16.4 - Prob. 28ESCh. 16.4 - Prob. 29ESCh. 16.4 - Prob. 30ESCh. 16.4 - Prob. 31ESCh. 16.4 - Prob. 32ESCh. 16.4 - Prob. 33ESCh. 16.4 - Prob. 34ESCh. 16.4 - Prob. 35ESCh. 16.4 - Prob. 36ESCh. 16.4 - Prob. 37ESCh. 16.4 - Prob. 38ESCh. 16.4 - Prob. 39ESCh. 16.4 - Prob. 40ESCh. 16.4 - Prob. 41ESCh. 16.4 - Prob. 42ESCh. 16.4 - Prob. 43ESCh. 16.4 - Prob. 44ESCh. 16.4 - Prob. 45ESCh. 16.4 - Prob. 46ESCh. 16.4 - Prob. 47ESCh. 16.4 - Prob. 48ESCh. 16.4 - Prob. 49ESCh. 16.4 - Prob. 50ESCh. 16.4 - Prob. 51ESCh. 16.4 - Prob. 52ESCh. 16.4 - Prob. 53ESCh. 16.4 - Prob. 54ESCh. 16.4 - Prob. 55ESCh. 16.4 - Prob. 56ESCh. 16.4 - Prob. 57ESCh. 16.4 - Prob. 58ESCh. 16.4 - Prob. 59ESCh. 16.4 - Prob. 60ESCh. 16.4 - Prob. 61ESCh. 16.4 - Prob. 62ESCh. 16.4 - Prob. 63ESCh. 16.4 - Prob. 64ESCh. 16.4 - Prob. 65ESCh. 16.4 - Prob. 66ESCh. 16.4 - Prob. 67ESCh. 16.4 - Prob. 68ESCh. 16.4 - Prob. 69ESCh. 16.4 - Prob. 70ESCh. 16.4 - Prob. 71ESCh. 16.4 - Prob. 72ESCh. 16.4 - Prob. 73ESCh. 16.4 - Prob. 74ESCh. 16.4 - Prob. 75ESCh. 16.4 - Prob. 76ESCh. 16.4 - Prob. 77ESCh. 16.4 - Prob. 78ESCh. 16.4 - Prob. 79ESCh. 16.4 - Prob. 80ESCh. 16.4 - Prob. 81ESCh. 16.4 - Prob. 82ESCh. 16.4 - Prob. 83ESCh. 16.4 - Prob. 84ESCh. 16.4 - Prob. 85ESCh. 16.4 - Prob. 86ESCh. 16.4 - Prob. 87ESCh. 16.4 - Prob. 88ESCh. 16.4 - Prob. 89ESCh. 16.4 - Prob. 90ESCh. 16.4 - Prob. 91ESCh. 16.4 - Prob. 92ESCh. 16.4 - Prob. 93ESCh. 16.4 - Prob. 94ESCh. 16.4 - Prob. 95ESCh. 16.4 - Prob. 96ESCh. 16.4 - Prob. 97ESCh. 16 - Prob. 1IRCh. 16 - Prob. 2IRCh. 16 - Prob. 3IRCh. 16 - Prob. 4IRCh. 16 - Prob. 5IRCh. 16 - Prob. 6IRCh. 16 - Prob. 7IRCh. 16 - Prob. 8IRCh. 16 - Prob. 9IRCh. 16 - Prob. 10IRCh. 16 - Prob. 11IRCh. 16 - Prob. 12IRCh. 16 - Prob. 13IRCh. 16 - Prob. 14IRCh. 16 - Prob. 15IRCh. 16 - Prob. 16IRCh. 16 - Prob. 17IRCh. 16 - Prob. 1VCCh. 16 - Prob. 2VCCh. 16 - Prob. 3VCCh. 16 - Prob. 4VCCh. 16 - Prob. 5VCCh. 16 - Prob. 6VCCh. 16 - Prob. 1RCh. 16 - Prob. 2RCh. 16 - Prob. 3RCh. 16 - Prob. 4RCh. 16 - Prob. 5RCh. 16 - Prob. 6RCh. 16 - Prob. 7RCh. 16 - Prob. 8RCh. 16 - Prob. 9RCh. 16 - Prob. 10RCh. 16 - Prob. 11RCh. 16 - Prob. 12RCh. 16 - Prob. 13RCh. 16 - Prob. 14RCh. 16 - Prob. 15RCh. 16 - Prob. 16RCh. 16 - Prob. 17RCh. 16 - Prob. 18RCh. 16 - Prob. 19RCh. 16 - Prob. 20RCh. 16 - Prob. 21RCh. 16 - Prob. 22RCh. 16 - Prob. 23RCh. 16 - Prob. 24RCh. 16 - Prob. 25RCh. 16 - Prob. 26RCh. 16 - Prob. 27RCh. 16 - Prob. 28RCh. 16 - Prob. 29RCh. 16 - Prob. 30RCh. 16 - Prob. 31RCh. 16 - Prob. 32RCh. 16 - Prob. 33RCh. 16 - Prob. 34RCh. 16 - Prob. 35RCh. 16 - Prob. 36RCh. 16 - Prob. 37RCh. 16 - Prob. 38RCh. 16 - Prob. 39RCh. 16 - Prob. 40RCh. 16 - Prob. 41RCh. 16 - Prob. 42RCh. 16 - Prob. 43RCh. 16 - Prob. 44RCh. 16 - 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