EBK ALGEBRA FOUNDATIONS
15th Edition
ISBN: 9780321978929
Author: Martin-Gay
Publisher: PEARSON
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Chapter 13.7, Problem 53ES
To determine
To write the fraction
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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 13 Solutions
EBK ALGEBRA FOUNDATIONS
Ch. 13.1 - Prob. 1VRVCCh. 13.1 - Prob. 2VRVCCh. 13.1 - Prob. 3VRVCCh. 13.1 - Prob. 4VRVCCh. 13.1 - Prob. 5VRVCCh. 13.1 - Prob. 6VRVCCh. 13.1 - Prob. 1ESCh. 13.1 - Prob. 2ESCh. 13.1 - Prob. 3ESCh. 13.1 - Prob. 4ES
Ch. 13.1 - Prob. 5ESCh. 13.1 - Prob. 6ESCh. 13.1 - Prob. 7ESCh. 13.1 - Prob. 8ESCh. 13.1 - Prob. 9ESCh. 13.1 - Prob. 10ESCh. 13.1 - Prob. 11ESCh. 13.1 - Prob. 12ESCh. 13.1 - Prob. 13ESCh. 13.1 - Prob. 14ESCh. 13.1 - Prob. 15ESCh. 13.1 - Prob. 16ESCh. 13.1 - Prob. 17ESCh. 13.1 - Prob. 18ESCh. 13.1 - Prob. 19ESCh. 13.1 - Prob. 20ESCh. 13.1 - Prob. 21ESCh. 13.1 - Prob. 22ESCh. 13.1 - Prob. 23ESCh. 13.1 - Prob. 24ESCh. 13.1 - Objective C Factor out the GCF from each...Ch. 13.1 - Objective C Factor out the GCF from each...Ch. 13.1 - Prob. 27ESCh. 13.1 - Prob. 28ESCh. 13.1 - Prob. 29ESCh. 13.1 - Prob. 30ESCh. 13.1 - Prob. 31ESCh. 13.1 - Prob. 32ESCh. 13.1 - Prob. 33ESCh. 13.1 - Prob. 34ESCh. 13.1 - Prob. 35ESCh. 13.1 - Prob. 36ESCh. 13.1 - Prob. 37ESCh. 13.1 - Prob. 38ESCh. 13.1 - Prob. 39ESCh. 13.1 - Prob. 40ESCh. 13.1 - Prob. 41ESCh. 13.1 - Prob. 42ESCh. 13.1 - Prob. 43ESCh. 13.1 - Prob. 44ESCh. 13.1 - Prob. 45ESCh. 13.1 - Prob. 46ESCh. 13.1 - Prob. 47ESCh. 13.1 - Prob. 48ESCh. 13.1 - Prob. 49ESCh. 13.1 - Prob. 50ESCh. 13.1 - Prob. 51ESCh. 13.1 - Prob. 52ESCh. 13.1 - Prob. 53ESCh. 13.1 - Prob. 54ESCh. 13.1 - Prob. 55ESCh. 13.1 - Prob. 56ESCh. 13.1 - Prob. 57ESCh. 13.1 - Prob. 58ESCh. 13.1 - Prob. 59ESCh. 13.1 - Prob. 60ESCh. 13.1 - Prob. 61ESCh. 13.1 - Prob. 62ESCh. 13.1 - Prob. 63ESCh. 13.1 - Prob. 64ESCh. 13.1 - Prob. 65ESCh. 13.1 - Prob. 66ESCh. 13.1 - Prob. 67ESCh. 13.1 - Prob. 68ESCh. 13.1 - Prob. 69ESCh. 13.1 - Prob. 70ESCh. 13.1 - Prob. 71ESCh. 13.1 - Prob. 72ESCh. 13.1 - Prob. 73ESCh. 13.1 - Prob. 74ESCh. 13.1 - Prob. 75ESCh. 13.1 - Prob. 76ESCh. 13.1 - Prob. 77ESCh. 13.1 - Prob. 78ESCh. 13.1 - Prob. 79ESCh. 13.1 - Prob. 80ESCh. 13.1 - Prob. 81ESCh. 13.1 - Factor. See Examples 4 through 17. 5x3y15x2y+10xyCh. 13.1 - Prob. 83ESCh. 13.1 - Prob. 84ESCh. 13.1 - Prob. 85ESCh. 13.1 - Prob. 86ESCh. 13.1 - Prob. 87ESCh. 13.1 - Prob. 88ESCh. 13.1 - Prob. 89ESCh. 13.1 - Prob. 90ESCh. 13.1 - Prob. 91ESCh. 13.1 - Prob. 92ESCh. 13.1 - Prob. 93ESCh. 13.1 - Prob. 94ESCh. 13.1 - Prob. 95ESCh. 13.1 - Prob. 96ESCh. 13.1 - Prob. 97ESCh. 13.1 - Prob. 98ESCh. 13.1 - Prob. 99ESCh. 13.1 - Prob. 100ESCh. 13.1 - Prob. 101ESCh. 13.1 - Prob. 102ESCh. 13.1 - Prob. 103ESCh. 13.1 - Prob. 104ESCh. 13.1 - Prob. 105ESCh. 13.1 - Prob. 106ESCh. 13.1 - Prob. 107ESCh. 13.1 - Prob. 108ESCh. 13.1 - Prob. 109ESCh. 13.1 - Prob. 110ESCh. 13.1 - Prob. 111ESCh. 13.1 - Prob. 112ESCh. 13.1 - Prob. 113ESCh. 13.1 - Prob. 114ESCh. 13.1 - Prob. 115ESCh. 13.1 - Prob. 116ESCh. 13.1 - Prob. 117ESCh. 13.1 - Prob. 118ESCh. 13.2 - Prob. 1VRVCCh. 13.2 - Prob. 2VRVCCh. 13.2 - Prob. 3VRVCCh. 13.2 - Prob. 4VRVCCh. 13.2 - Prob. 5VRVCCh. 13.2 - Prob. 6VRVCCh. 13.2 - Prob. 7VRVCCh. 13.2 - Prob. 8VRVCCh. 13.2 - Prob. 9VRVCCh. 13.2 - Prob. 10VRVCCh. 13.2 - Prob. 1ESCh. 13.2 - Prob. 2ESCh. 13.2 - Prob. 3ESCh. 13.2 - Prob. 4ESCh. 13.2 - Prob. 5ESCh. 13.2 - Prob. 6ESCh. 13.2 - Prob. 7ESCh. 13.2 - Prob. 8ESCh. 13.2 - Prob. 9ESCh. 13.2 - Prob. 10ESCh. 13.2 - Prob. 11ESCh. 13.2 - Prob. 12ESCh. 13.2 - Prob. 13ESCh. 13.2 - Prob. 14ESCh. 13.2 - Prob. 15ESCh. 13.2 - Prob. 16ESCh. 13.2 - Prob. 17ESCh. 13.2 - Prob. 18ESCh. 13.2 - Prob. 19ESCh. 13.2 - Prob. 20ESCh. 13.2 - Prob. 21ESCh. 13.2 - Prob. 22ESCh. 13.2 - Prob. 23ESCh. 13.2 - Prob. 24ESCh. 13.2 - Prob. 25ESCh. 13.2 - Prob. 26ESCh. 13.2 - Prob. 27ESCh. 13.2 - Prob. 28ESCh. 13.2 - Prob. 29ESCh. 13.2 - Prob. 30ESCh. 13.2 - Prob. 31ESCh. 13.2 - Prob. 32ESCh. 13.2 - Prob. 33ESCh. 13.2 - Prob. 34ESCh. 13.2 - Prob. 35ESCh. 13.2 - Prob. 36ESCh. 13.2 - Prob. 37ESCh. 13.2 - Prob. 38ESCh. 13.2 - Prob. 39ESCh. 13.2 - Prob. 40ESCh. 13.2 - Prob. 41ESCh. 13.2 - Prob. 42ESCh. 13.2 - Prob. 43ESCh. 13.2 - Prob. 44ESCh. 13.2 - Prob. 45ESCh. 13.2 - Prob. 46ESCh. 13.2 - Prob. 47ESCh. 13.2 - Prob. 48ESCh. 13.2 - Prob. 49ESCh. 13.2 - Prob. 50ESCh. 13.2 - Prob. 51ESCh. 13.2 - Prob. 52ESCh. 13.2 - Prob. 53ESCh. 13.2 - Prob. 54ESCh. 13.2 - Prob. 55ESCh. 13.2 - Prob. 56ESCh. 13.2 - Prob. 57ESCh. 13.2 - Prob. 58ESCh. 13.2 - Prob. 59ESCh. 13.2 - Prob. 60ESCh. 13.2 - Prob. 61ESCh. 13.2 - Prob. 62ESCh. 13.2 - Prob. 63ESCh. 13.2 - Prob. 64ESCh. 13.2 - Prob. 65ESCh. 13.2 - Prob. 66ESCh. 13.2 - Prob. 67ESCh. 13.2 - Prob. 68ESCh. 13.2 - Prob. 69ESCh. 13.2 - Prob. 70ESCh. 13.2 - Prob. 71ESCh. 13.2 - Prob. 72ESCh. 13.2 - Prob. 73ESCh. 13.2 - Prob. 74ESCh. 13.2 - Prob. 75ESCh. 13.2 - Prob. 76ESCh. 13.2 - Prob. 77ESCh. 13.2 - Prob. 78ESCh. 13.2 - Prob. 79ESCh. 13.2 - Prob. 80ESCh. 13.2 - Prob. 81ESCh. 13.2 - Prob. 82ESCh. 13.2 - Prob. 83ESCh. 13.2 - Prob. 84ESCh. 13.2 - Prob. 85ESCh. 13.2 - Prob. 86ESCh. 13.2 - Prob. 87ESCh. 13.2 - Prob. 88ESCh. 13.2 - Prob. 89ESCh. 13.2 - Prob. 90ESCh. 13.2 - Prob. 91ESCh. 13.2 - Prob. 92ESCh. 13.2 - Prob. 93ESCh. 13.2 - Prob. 94ESCh. 13.2 - Prob. 95ESCh. 13.2 - Prob. 96ESCh. 13.2 - Prob. 97ESCh. 13.2 - Prob. 98ESCh. 13.3 - Use the choices below to fill in each blank. Some...Ch. 13.3 - Prob. 2VRVCCh. 13.3 - Prob. 3VRVCCh. 13.3 - Prob. 4VRVCCh. 13.3 - Prob. 5VRVCCh. 13.3 - Prob. 6VRVCCh. 13.3 - Prob. 1ESCh. 13.3 - Prob. 2ESCh. 13.3 - Prob. 3ESCh. 13.3 - Prob. 4ESCh. 13.3 - Prob. 5ESCh. 13.3 - Prob. 6ESCh. 13.3 - Prob. 7ESCh. 13.3 - Prob. 8ESCh. 13.3 - Prob. 9ESCh. 13.3 - Prob. 10ESCh. 13.3 - Prob. 11ESCh. 13.3 - Prob. 12ESCh. 13.3 - Prob. 13ESCh. 13.3 - Prob. 14ESCh. 13.3 - Prob. 15ESCh. 13.3 - Prob. 16ESCh. 13.3 - Prob. 17ESCh. 13.3 - Prob. 18ESCh. 13.3 - Prob. 19ESCh. 13.3 - Prob. 20ESCh. 13.3 - Prob. 21ESCh. 13.3 - Prob. 22ESCh. 13.3 - Prob. 23ESCh. 13.3 - Prob. 24ESCh. 13.3 - Prob. 25ESCh. 13.3 - Prob. 26ESCh. 13.3 - Prob. 27ESCh. 13.3 - Prob. 28ESCh. 13.3 - Prob. 29ESCh. 13.3 - Prob. 30ESCh. 13.3 - Prob. 31ESCh. 13.3 - Prob. 32ESCh. 13.3 - Prob. 33ESCh. 13.3 - Prob. 34ESCh. 13.3 - Prob. 35ESCh. 13.3 - Prob. 36ESCh. 13.3 - Prob. 37ESCh. 13.3 - Prob. 38ESCh. 13.3 - Prob. 39ESCh. 13.3 - Prob. 40ESCh. 13.3 - Prob. 41ESCh. 13.3 - Prob. 42ESCh. 13.3 - Prob. 43ESCh. 13.3 - Prob. 44ESCh. 13.3 - Prob. 45ESCh. 13.3 - Prob. 46ESCh. 13.3 - Prob. 47ESCh. 13.3 - Prob. 48ESCh. 13.3 - Prob. 49ESCh. 13.3 - Prob. 50ESCh. 13.3 - Prob. 51ESCh. 13.3 - Prob. 52ESCh. 13.3 - Prob. 53ESCh. 13.3 - Prob. 54ESCh. 13.3 - Prob. 55ESCh. 13.3 - Prob. 56ESCh. 13.3 - Prob. 57ESCh. 13.3 - Prob. 58ESCh. 13.3 - Prob. 59ESCh. 13.3 - Prob. 60ESCh. 13.3 - Prob. 61ESCh. 13.3 - Prob. 62ESCh. 13.3 - Prob. 63ESCh. 13.3 - Prob. 64ESCh. 13.3 - Prob. 65ESCh. 13.3 - Prob. 66ESCh. 13.3 - Prob. 67ESCh. 13.3 - Prob. 68ESCh. 13.3 - Prob. 69ESCh. 13.3 - Prob. 70ESCh. 13.3 - Prob. 71ESCh. 13.3 - Prob. 72ESCh. 13.3 - Prob. 73ESCh. 13.3 - Prob. 74ESCh. 13.3 - Prob. 75ESCh. 13.3 - Prob. 76ESCh. 13.3 - Prob. 77ESCh. 13.3 - Prob. 78ESCh. 13.3 - Prob. 79ESCh. 13.3 - Prob. 80ESCh. 13.3 - Prob. 81ESCh. 13.3 - Prob. 82ESCh. 13.3 - Prob. 83ESCh. 13.3 - Prob. 84ESCh. 13.3 - Prob. 85ESCh. 13.3 - Prob. 86ESCh. 13.3 - Prob. 87ESCh. 13.3 - Prob. 88ESCh. 13.3 - Prob. 89ESCh. 13.3 - Prob. 90ESCh. 13.3 - Prob. 91ESCh. 13.3 - Prob. 92ESCh. 13.3 - Prob. 93ESCh. 13.3 - Prob. 94ESCh. 13.3 - Prob. 95ESCh. 13.3 - Prob. 96ESCh. 13.3 - Prob. 97ESCh. 13.3 - Prob. 98ESCh. 13.3 - Prob. 99ESCh. 13.3 - Prob. 100ESCh. 13.3 - Prob. 101ESCh. 13.3 - Prob. 102ESCh. 13.3 - Prob. 103ESCh. 13.3 - Prob. 104ESCh. 13.3 - Prob. 105ESCh. 13.3 - Prob. 106ESCh. 13.3 - Prob. 107ESCh. 13.3 - Prob. 108ESCh. 13.3 - Prob. 109ESCh. 13.3 - Prob. 110ESCh. 13.3 - Prob. 111ESCh. 13.3 - Prob. 112ESCh. 13.3 - Prob. 113ESCh. 13.3 - Prob. 114ESCh. 13.3 - Prob. 115ESCh. 13.3 - Prob. 116ESCh. 13.3 - Prob. 117ESCh. 13.3 - Prob. 118ESCh. 13.3 - Prob. 119ESCh. 13.3 - Prob. 120ESCh. 13.3 - Prob. 121ESCh. 13.3 - Prob. 122ESCh. 13.3 - Prob. 123ESCh. 13.3 - Prob. 124ESCh. 13.3 - Prob. 125ESCh. 13.3 - Prob. 126ESCh. 13.3 - Prob. 127ESCh. 13.4 - Prob. 1VRVCCh. 13.4 - Prob. 2VRVCCh. 13.4 - Prob. 3VRVCCh. 13.4 - Prob. 4VRVCCh. 13.4 - Prob. 1ESCh. 13.4 - Prob. 2ESCh. 13.4 - Prob. 3ESCh. 13.4 - Prob. 4ESCh. 13.4 - Prob. 5ESCh. 13.4 - Prob. 6ESCh. 13.4 - Prob. 7ESCh. 13.4 - Prob. 8ESCh. 13.4 - Prob. 9ESCh. 13.4 - Prob. 10ESCh. 13.4 - Prob. 11ESCh. 13.4 - Prob. 12ESCh. 13.4 - Prob. 13ESCh. 13.4 - Prob. 14ESCh. 13.4 - Prob. 15ESCh. 13.4 - Prob. 16ESCh. 13.4 - Prob. 17ESCh. 13.4 - Prob. 18ESCh. 13.4 - Prob. 19ESCh. 13.4 - Prob. 20ESCh. 13.4 - Prob. 21ESCh. 13.4 - Prob. 22ESCh. 13.4 - Prob. 23ESCh. 13.4 - Prob. 24ESCh. 13.4 - Prob. 25ESCh. 13.4 - Prob. 26ESCh. 13.4 - Prob. 27ESCh. 13.4 - Prob. 28ESCh. 13.4 - Prob. 29ESCh. 13.4 - Prob. 30ESCh. 13.4 - Prob. 31ESCh. 13.4 - Prob. 32ESCh. 13.4 - Prob. 33ESCh. 13.4 - Prob. 34ESCh. 13.4 - Prob. 35ESCh. 13.4 - Prob. 36ESCh. 13.4 - Prob. 37ESCh. 13.4 - Prob. 38ESCh. 13.4 - Prob. 39ESCh. 13.4 - Prob. 40ESCh. 13.4 - Prob. 41ESCh. 13.4 - Prob. 42ESCh. 13.4 - Prob. 43ESCh. 13.4 - Prob. 44ESCh. 13.4 - Prob. 45ESCh. 13.4 - Prob. 46ESCh. 13.4 - Prob. 47ESCh. 13.4 - Prob. 48ESCh. 13.4 - Prob. 49ESCh. 13.4 - Prob. 50ESCh. 13.4 - Prob. 51ESCh. 13.4 - Prob. 52ESCh. 13.4 - Prob. 53ESCh. 13.4 - Prob. 54ESCh. 13.4 - Prob. 55ESCh. 13.4 - Prob. 56ESCh. 13.4 - Prob. 57ESCh. 13.4 - Prob. 58ESCh. 13.4 - Prob. 59ESCh. 13.4 - Prob. 60ESCh. 13.4 - Prob. 61ESCh. 13.4 - Prob. 62ESCh. 13.4 - Prob. 63ESCh. 13.4 - Prob. 64ESCh. 13.4 - Prob. 65ESCh. 13.4 - Prob. 66ESCh. 13.4 - Prob. 67ESCh. 13.4 - Prob. 68ESCh. 13.4 - Prob. 69ESCh. 13.5 - Prob. 1VRVCCh. 13.5 - Prob. 2VRVCCh. 13.5 - Prob. 3VRVCCh. 13.5 - Prob. 4VRVCCh. 13.5 - Prob. 5VRVCCh. 13.5 - Prob. 6VRVCCh. 13.5 - Prob. 7VRVCCh. 13.5 - Prob. 8VRVCCh. 13.5 - Prob. 1ESCh. 13.5 - Prob. 2ESCh. 13.5 - Prob. 3ESCh. 13.5 - Prob. 4ESCh. 13.5 - Prob. 5ESCh. 13.5 - Prob. 6ESCh. 13.5 - Prob. 7ESCh. 13.5 - Prob. 8ESCh. 13.5 - Prob. 9ESCh. 13.5 - Prob. 10ESCh. 13.5 - Prob. 11ESCh. 13.5 - Prob. 12ESCh. 13.5 - Prob. 13ESCh. 13.5 - Prob. 14ESCh. 13.5 - Prob. 15ESCh. 13.5 - Prob. 16ESCh. 13.5 - Prob. 17ESCh. 13.5 - Prob. 18ESCh. 13.5 - Prob. 19ESCh. 13.5 - Prob. 20ESCh. 13.5 - Prob. 21ESCh. 13.5 - Prob. 22ESCh. 13.5 - Prob. 23ESCh. 13.5 - Prob. 24ESCh. 13.5 - Prob. 25ESCh. 13.5 - Prob. 26ESCh. 13.5 - Prob. 27ESCh. 13.5 - Prob. 28ESCh. 13.5 - Prob. 29ESCh. 13.5 - Prob. 30ESCh. 13.5 - Prob. 31ESCh. 13.5 - Prob. 32ESCh. 13.5 - Prob. 33ESCh. 13.5 - Prob. 34ESCh. 13.5 - Prob. 35ESCh. 13.5 - Prob. 36ESCh. 13.5 - Prob. 37ESCh. 13.5 - Prob. 38ESCh. 13.5 - Prob. 39ESCh. 13.5 - Prob. 40ESCh. 13.5 - Prob. 41ESCh. 13.5 - Prob. 42ESCh. 13.5 - Prob. 43ESCh. 13.5 - Prob. 44ESCh. 13.5 - Prob. 45ESCh. 13.5 - Prob. 46ESCh. 13.5 - Prob. 47ESCh. 13.5 - Prob. 48ESCh. 13.5 - Prob. 49ESCh. 13.5 - Prob. 50ESCh. 13.5 - Prob. 51ESCh. 13.5 - Prob. 52ESCh. 13.5 - Prob. 53ESCh. 13.5 - Prob. 54ESCh. 13.5 - Prob. 55ESCh. 13.5 - Prob. 56ESCh. 13.5 - Prob. 57ESCh. 13.5 - Prob. 58ESCh. 13.5 - Prob. 59ESCh. 13.5 - Prob. 60ESCh. 13.5 - Prob. 61ESCh. 13.5 - Prob. 62ESCh. 13.5 - Prob. 63ESCh. 13.5 - Prob. 64ESCh. 13.5 - Prob. 65ESCh. 13.5 - Prob. 66ESCh. 13.5 - Prob. 67ESCh. 13.5 - Prob. 68ESCh. 13.5 - Prob. 69ESCh. 13.5 - Prob. 70ESCh. 13.5 - Prob. 71ESCh. 13.5 - Prob. 72ESCh. 13.5 - Prob. 73ESCh. 13.5 - Prob. 74ESCh. 13.5 - Prob. 75ESCh. 13.5 - Prob. 76ESCh. 13.5 - Prob. 77ESCh. 13.5 - Prob. 78ESCh. 13.5 - Prob. 79ESCh. 13.5 - Prob. 80ESCh. 13.5 - Prob. 81ESCh. 13.5 - Prob. 82ESCh. 13.5 - Prob. 83ESCh. 13.5 - Prob. 84ESCh. 13.5 - Prob. 85ESCh. 13.5 - Prob. 86ESCh. 13.5 - Prob. 87ESCh. 13.5 - Prob. 88ESCh. 13.5 - Prob. 90ESCh. 13.5 - Prob. 91ESCh. 13.5 - Prob. 92ESCh. 13.6 - Prob. 1VRVCCh. 13.6 - Prob. 2VRVCCh. 13.6 - Prob. 3VRVCCh. 13.6 - Prob. 4VRVCCh. 13.6 - Prob. 1ESCh. 13.6 - Prob. 2ESCh. 13.6 - Prob. 3ESCh. 13.6 - Prob. 4ESCh. 13.6 - Prob. 5ESCh. 13.6 - Prob. 6ESCh. 13.6 - Prob. 7ESCh. 13.6 - Prob. 8ESCh. 13.6 - Prob. 9ESCh. 13.6 - Prob. 10ESCh. 13.6 - Prob. 11ESCh. 13.6 - Prob. 12ESCh. 13.6 - Prob. 13ESCh. 13.6 - Prob. 14ESCh. 13.6 - Prob. 15ESCh. 13.6 - Prob. 16ESCh. 13.6 - Prob. 17ESCh. 13.6 - Prob. 18ESCh. 13.6 - Prob. 19ESCh. 13.6 - Prob. 20ESCh. 13.6 - Prob. 21ESCh. 13.6 - Prob. 22ESCh. 13.6 - Prob. 23ESCh. 13.6 - Prob. 24ESCh. 13.6 - Prob. 25ESCh. 13.6 - Prob. 26ESCh. 13.6 - Prob. 27ESCh. 13.6 - Prob. 28ESCh. 13.6 - Prob. 29ESCh. 13.6 - Prob. 30ESCh. 13.6 - Prob. 31ESCh. 13.6 - Prob. 32ESCh. 13.6 - Prob. 33ESCh. 13.6 - Prob. 34ESCh. 13.6 - Prob. 35ESCh. 13.6 - Prob. 36ESCh. 13.6 - Prob. 37ESCh. 13.6 - Prob. 38ESCh. 13.6 - Prob. 39ESCh. 13.6 - Prob. 40ESCh. 13.6 - Prob. 41ESCh. 13.6 - Prob. 42ESCh. 13.6 - Prob. 43ESCh. 13.6 - Prob. 44ESCh. 13.6 - Prob. 45ESCh. 13.6 - Prob. 46ESCh. 13.6 - Prob. 47ESCh. 13.6 - Prob. 48ESCh. 13.6 - Prob. 49ESCh. 13.6 - Prob. 50ESCh. 13.6 - Prob. 51ESCh. 13.6 - Prob. 52ESCh. 13.6 - Prob. 53ESCh. 13.6 - Prob. 54ESCh. 13.6 - Prob. 55ESCh. 13.6 - Prob. 56ESCh. 13.6 - Prob. 57ESCh. 13.6 - Prob. 58ESCh. 13.6 - Prob. 59ESCh. 13.6 - Prob. 60ESCh. 13.6 - Prob. 61ESCh. 13.6 - Prob. 62ESCh. 13.6 - Prob. 63ESCh. 13.6 - Prob. 64ESCh. 13.6 - Prob. 65ESCh. 13.6 - Prob. 66ESCh. 13.6 - Prob. 67ESCh. 13.6 - Prob. 68ESCh. 13.6 - Prob. 69ESCh. 13.6 - Prob. 70ESCh. 13.6 - Prob. 71ESCh. 13.6 - Prob. 72ESCh. 13.6 - Prob. 73ESCh. 13.6 - Prob. 74ESCh. 13.6 - Prob. 75ESCh. 13.6 - Prob. 76ESCh. 13.6 - Prob. 77ESCh. 13.6 - Prob. 78ESCh. 13.6 - Prob. 79ESCh. 13.6 - Prob. 80ESCh. 13.6 - Prob. 81ESCh. 13.6 - Prob. 82ESCh. 13.6 - Prob. 83ESCh. 13.6 - Prob. 84ESCh. 13.6 - Prob. 85ESCh. 13.6 - Prob. 86ESCh. 13.6 - Prob. 87ESCh. 13.6 - Prob. 88ESCh. 13.6 - Prob. 89ESCh. 13.6 - Prob. 90ESCh. 13.6 - Prob. 91ESCh. 13.6 - Perform the following operations. Write all...Ch. 13.6 - Prob. 93ESCh. 13.6 - Prob. 94ESCh. 13.6 - Prob. 95ESCh. 13.6 - Prob. 96ESCh. 13.6 - Prob. 97ESCh. 13.6 - Prob. 98ESCh. 13.6 - Prob. 99ESCh. 13.6 - Prob. 100ESCh. 13.6 - Prob. 101ESCh. 13.6 - Prob. 102ESCh. 13.6 - Prob. 103ESCh. 13.6 - A rocket is fired upward from the ground with an...Ch. 13.6 - Prob. 105ESCh. 13.6 - Prob. 106ESCh. 13.6 - Prob. 107ESCh. 13.6 - Prob. 108ESCh. 13.7 - Prob. 1ESCh. 13.7 - Prob. 2ESCh. 13.7 - Prob. 3ESCh. 13.7 - Prob. 4ESCh. 13.7 - Prob. 5ESCh. 13.7 - Prob. 6ESCh. 13.7 - Prob. 7ESCh. 13.7 - Prob. 8ESCh. 13.7 - Prob. 9ESCh. 13.7 - Prob. 10ESCh. 13.7 - Prob. 11ESCh. 13.7 - Prob. 12ESCh. 13.7 - Prob. 13ESCh. 13.7 - Prob. 14ESCh. 13.7 - Prob. 15ESCh. 13.7 - Prob. 16ESCh. 13.7 - Prob. 17ESCh. 13.7 - Prob. 18ESCh. 13.7 - Prob. 19ESCh. 13.7 - Prob. 20ESCh. 13.7 - Prob. 21ESCh. 13.7 - Prob. 22ESCh. 13.7 - Prob. 23ESCh. 13.7 - Prob. 24ESCh. 13.7 - Prob. 25ESCh. 13.7 - Prob. 26ESCh. 13.7 - Prob. 27ESCh. 13.7 - Prob. 28ESCh. 13.7 - Prob. 29ESCh. 13.7 - Prob. 30ESCh. 13.7 - Prob. 31ESCh. 13.7 - Prob. 32ESCh. 13.7 - Prob. 33ESCh. 13.7 - Prob. 34ESCh. 13.7 - Prob. 35ESCh. 13.7 - Prob. 36ESCh. 13.7 - Prob. 37ESCh. 13.7 - Prob. 38ESCh. 13.7 - Prob. 39ESCh. 13.7 - Prob. 40ESCh. 13.7 - Prob. 41ESCh. 13.7 - Prob. 42ESCh. 13.7 - Prob. 43ESCh. 13.7 - Prob. 44ESCh. 13.7 - Prob. 45ESCh. 13.7 - Prob. 46ESCh. 13.7 - Prob. 47ESCh. 13.7 - Prob. 48ESCh. 13.7 - Prob. 49ESCh. 13.7 - Prob. 50ESCh. 13.7 - Prob. 51ESCh. 13.7 - Prob. 52ESCh. 13.7 - Prob. 53ESCh. 13.7 - Prob. 54ESCh. 13.7 - Prob. 55ESCh. 13.7 - Prob. 56ESCh. 13.7 - Prob. 57ESCh. 13.7 - Prob. 58ESCh. 13.7 - Prob. 59ESCh. 13.7 - Prob. 60ESCh. 13.7 - Prob. 61ESCh. 13.7 - Prob. 62ESCh. 13.7 - Prob. 63ESCh. 13.7 - Prob. 64ESCh. 13 - Prob. 1IRCh. 13 - Prob. 2IRCh. 13 - Factor the following completely. 3.a2+11a12Ch. 13 - Prob. 4IRCh. 13 - Prob. 5IRCh. 13 - Prob. 6IRCh. 13 - Prob. 7IRCh. 13 - Prob. 8IRCh. 13 - Prob. 9IRCh. 13 - Factor the following completely. 10. x2+x6Ch. 13 - Prob. 11IRCh. 13 - Prob. 12IRCh. 13 - Prob. 13IRCh. 13 - Prob. 14IRCh. 13 - Prob. 15IRCh. 13 - Prob. 16IRCh. 13 - Factor the following completely. 17. x2x30Ch. 13 - Prob. 18IRCh. 13 - Prob. 19IRCh. 13 - Prob. 20IRCh. 13 - Prob. 21IRCh. 13 - Prob. 22IRCh. 13 - Prob. 23IRCh. 13 - Prob. 24IRCh. 13 - Prob. 25IRCh. 13 - Prob. 26IRCh. 13 - Prob. 27IRCh. 13 - Prob. 28IRCh. 13 - Prob. 29IRCh. 13 - Prob. 30IRCh. 13 - Factor the following completely. 31. 203x2x2Ch. 13 - Prob. 32IRCh. 13 - Prob. 33IRCh. 13 - Prob. 34IRCh. 13 - Prob. 35IRCh. 13 - Prob. 36IRCh. 13 - Prob. 37IRCh. 13 - Prob. 38IRCh. 13 - Prob. 39IRCh. 13 - Prob. 40IRCh. 13 - Prob. 41IRCh. 13 - Prob. 42IRCh. 13 - Prob. 43IRCh. 13 - Prob. 44IRCh. 13 - Prob. 45IRCh. 13 - Prob. 46IRCh. 13 - Prob. 47IRCh. 13 - Prob. 48IRCh. 13 - Prob. 49IRCh. 13 - Prob. 50IRCh. 13 - Prob. 51IRCh. 13 - Prob. 52IRCh. 13 - Prob. 53IRCh. 13 - Prob. 54IRCh. 13 - Prob. 55IRCh. 13 - Prob. 56IRCh. 13 - Prob. 57IRCh. 13 - Prob. 58IRCh. 13 - Prob. 59IRCh. 13 - Prob. 60IRCh. 13 - Prob. 61IRCh. 13 - Prob. 62IRCh. 13 - Prob. 63IRCh. 13 - Prob. 64IRCh. 13 - Prob. 65IRCh. 13 - Prob. 66IRCh. 13 - Prob. 67IRCh. 13 - Prob. 68IRCh. 13 - Prob. 69IRCh. 13 - Prob. 70IRCh. 13 - Prob. 71IRCh. 13 - Prob. 72IRCh. 13 - Prob. 73IRCh. 13 - Prob. 74IRCh. 13 - Factor the following completely. 75. x2+9xy36y2Ch. 13 - Prob. 76IRCh. 13 - Prob. 77IRCh. 13 - Prob. 78IRCh. 13 - Prob. 79IRCh. 13 - Prob. 80IRCh. 13 - Prob. 81IRCh. 13 - Prob. 82IRCh. 13 - Prob. 83IRCh. 13 - Prob. 84IRCh. 13 - Prob. 85IRCh. 13 - Prob. 86IRCh. 13 - Prob. 87IRCh. 13 - Prob. 88IRCh. 13 - Prob. 89IRCh. 13 - Prob. 90IRCh. 13 - Prob. 91IRCh. 13 - Prob. 92IRCh. 13 - Prob. 93IRCh. 13 - Prob. 94IRCh. 13 - Prob. 95IRCh. 13 - Prob. 96IRCh. 13 - Prob. 97IRCh. 13 - Prob. 98IRCh. 13 - Prob. 99IRCh. 13 - Prob. 100IRCh. 13 - Prob. 101IRCh. 13 - Prob. 102IRCh. 13 - Prob. 103IRCh. 13 - Prob. 104IRCh. 13 - Explain why it makes good sense to factor out the...Ch. 13 - Prob. 106IRCh. 13 - Prob. 107IRCh. 13 - Prob. 108IRCh. 13 - Prob. 1VCCh. 13 - Prob. 2VCCh. 13 - Prob. 3VCCh. 13 - Prob. 4VCCh. 13 - Prob. 5VCCh. 13 - Prob. 6VCCh. 13 - Prob. 7VCCh. 13 - Prob. 8VCCh. 13 - Prob. 9VCCh. 13 - Fill in each blank with one of the words or...Ch. 13 - Prob. 11VCCh. 13 - Prob. 1RCh. 13 - Prob. 2RCh. 13 - Prob. 3RCh. 13 - Prob. 4RCh. 13 - Prob. 5RCh. 13 - Prob. 6RCh. 13 - Prob. 7RCh. 13 - Prob. 8RCh. 13 - Prob. 9RCh. 13 - Prob. 10RCh. 13 - Prob. 11RCh. 13 - Prob. 12RCh. 13 - Prob. 13RCh. 13 - Prob. 14RCh. 13 - Prob. 15RCh. 13 - Prob. 16RCh. 13 - Prob. 17RCh. 13 - Prob. 18RCh. 13 - Prob. 19RCh. 13 - Prob. 20RCh. 13 - Prob. 21RCh. 13 - Prob. 22RCh. 13 - Prob. 23RCh. 13 - Prob. 24RCh. 13 - Prob. 25RCh. 13 - Prob. 26RCh. 13 - Prob. 27RCh. 13 - Prob. 28RCh. 13 - Prob. 29RCh. 13 - Prob. 30RCh. 13 - Prob. 31RCh. 13 - Prob. 32RCh. 13 - Prob. 33RCh. 13 - Prob. 34RCh. 13 - Prob. 35RCh. 13 - Prob. 36RCh. 13 - Prob. 37RCh. 13 - Prob. 38RCh. 13 - Prob. 39RCh. 13 - Prob. 40RCh. 13 - Prob. 41RCh. 13 - Prob. 42RCh. 13 - Prob. 43RCh. 13 - Solve the following equations. 44. x2+8x+7=0Ch. 13 - Prob. 45RCh. 13 - Solve the following equations. 46. x2+10x=25Ch. 13 - Prob. 47RCh. 13 - Prob. 48RCh. 13 - Prob. 49RCh. 13 - Prob. 50RCh. 13 - Prob. 51RCh. 13 - Prob. 52RCh. 13 - Prob. 53RCh. 13 - Prob. 54RCh. 13 - Solve the following equations. 55. 4t35t221t=0Ch. 13 - Solve the following equations. 56. Write a...Ch. 13 - Prob. 57RCh. 13 - Prob. 58RCh. 13 - Prob. 59RCh. 13 - Prob. 60RCh. 13 - Prob. 61RCh. 13 - Prob. 62RCh. 13 - Prob. 63RCh. 13 - Prob. 64RCh. 13 - Prob. 65RCh. 13 - Prob. 66RCh. 13 - Prob. 67RCh. 13 - Prob. 68RCh. 13 - Prob. 69RCh. 13 - Prob. 70RCh. 13 - Prob. 71RCh. 13 - Prob. 72RCh. 13 - Prob. 73RCh. 13 - Prob. 74RCh. 13 - Prob. 75RCh. 13 - Prob. 76RCh. 13 - Prob. 77RCh. 13 - Prob. 78RCh. 13 - Prob. 79RCh. 13 - Prob. 80RCh. 13 - Prob. 81RCh. 13 - Prob. 82RCh. 13 - Prob. 83RCh. 13 - Prob. 84RCh. 13 - Prob. 85RCh. 13 - Prob. 86RCh. 13 - Prob. 87RCh. 13 - Prob. 88RCh. 13 - Prob. 89RCh. 13 - Prob. 90RCh. 13 - Prob. 91RCh. 13 - Prob. 92RCh. 13 - Prob. 93RCh. 13 - Prob. 94RCh. 13 - Prob. 95RCh. 13 - Prob. 1TCh. 13 - Factor each polynomial completely. If a polynomial...Ch. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - Prob. 5TCh. 13 - Prob. 6TCh. 13 - Prob. 7TCh. 13 - Prob. 8TCh. 13 - Prob. 9TCh. 13 - Prob. 10TCh. 13 - Prob. 11TCh. 13 - Prob. 12TCh. 13 - Prob. 13TCh. 13 - Prob. 14TCh. 13 - Prob. 15TCh. 13 - Factor each polynomial completely. If a polynomial...Ch. 13 - Prob. 17TCh. 13 - Prob. 18TCh. 13 - Prob. 19TCh. 13 - Prob. 20TCh. 13 - Prob. 21TCh. 13 - Prob. 22TCh. 13 - Prob. 23TCh. 13 - Prob. 24TCh. 13 - Prob. 25TCh. 13 - Prob. 26TCh. 13 - Prob. 27TCh. 13 - Prob. 28TCh. 13 - Solve each problem. 29. Find the lengths of the...Ch. 13 - Prob. 1CRCh. 13 - Prob. 2CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Evaluate y+5x if x=20 and y=10.Ch. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Prob. 11CRCh. 13 - Prob. 12CRCh. 13 - Prob. 13CRCh. 13 - Prob. 14CRCh. 13 - Prob. 15CRCh. 13 - Prob. 16CRCh. 13 - Prob. 17CRCh. 13 - Prob. 18CRCh. 13 - A 10-foot board is to be cut into two pieces so...Ch. 13 - Prob. 20CRCh. 13 - Prob. 21CRCh. 13 - Prob. 22CRCh. 13 - Prob. 23CRCh. 13 - Prob. 24CRCh. 13 - Prob. 25CRCh. 13 - Prob. 26CRCh. 13 - Prob. 27CRCh. 13 - Prob. 28CRCh. 13 - Prob. 29CRCh. 13 - Prob. 30CRCh. 13 - Prob. 31CRCh. 13 - Prob. 32CRCh. 13 - Prob. 33CRCh. 13 - Prob. 34CRCh. 13 - Prob. 35CRCh. 13 - Prob. 36CRCh. 13 - Prob. 37CRCh. 13 - Prob. 38CRCh. 13 - Prob. 39CRCh. 13 - Prob. 40CRCh. 13 - Prob. 41CRCh. 13 - Prob. 42CRCh. 13 - Prob. 43CRCh. 13 - Prob. 44CRCh. 13 - Prob. 45CRCh. 13 - Prob. 46CRCh. 13 - Prob. 47CRCh. 13 - Prob. 48CRCh. 13 - Prob. 49CRCh. 13 - 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
- Question 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_forwardTools 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_forward
- 2. 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_forwardI have ai answers but incorrectarrow_forward
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