College Algebra (10th Edition)
10th Edition
ISBN: 9780321979476
Author: Michael Sullivan
Publisher: PEARSON
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Chapter 1.6, Problem 21SB
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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 1 Solutions
College Algebra (10th Edition)
Ch. 1.1 - Prob. 1AYPCh. 1.1 - Prob. 2AYPCh. 1.1 - Prob. 3AYPCh. 1.1 - Prob. 4CVCh. 1.1 - Prob. 5CVCh. 1.1 - Prob. 6CVCh. 1.1 - Prob. 7CVCh. 1.1 - Prob. 8CVCh. 1.1 - Prob. 9CVCh. 1.1 - Prob. 10CV
Ch. 1.1 - Prob. 11SBCh. 1.1 - Prob. 12SBCh. 1.1 - Prob. 13SBCh. 1.1 - Prob. 14SBCh. 1.1 - Prob. 15SBCh. 1.1 - Prob. 16SBCh. 1.1 - Prob. 17SBCh. 1.1 - Prob. 18SBCh. 1.1 - Prob. 19SBCh. 1.1 - Prob. 20SBCh. 1.1 - Prob. 21SBCh. 1.1 - Prob. 22SBCh. 1.1 - Prob. 23SBCh. 1.1 - Prob. 24SBCh. 1.1 - Prob. 25SBCh. 1.1 - Prob. 26SBCh. 1.1 - Prob. 27SBCh. 1.1 - Prob. 28SBCh. 1.1 - Prob. 29SBCh. 1.1 - Prob. 30SBCh. 1.1 - Prob. 31SBCh. 1.1 - Prob. 32SBCh. 1.1 - Prob. 33SBCh. 1.1 - Prob. 34SBCh. 1.1 - Prob. 35SBCh. 1.1 - Prob. 36SBCh. 1.1 - Prob. 37SBCh. 1.1 - Prob. 38SBCh. 1.1 - Prob. 39SBCh. 1.1 - Prob. 40SBCh. 1.1 - Prob. 41SBCh. 1.1 - Prob. 42SBCh. 1.1 - Prob. 43SBCh. 1.1 - Prob. 44SBCh. 1.1 - Prob. 45SBCh. 1.1 - Prob. 46SBCh. 1.1 - Prob. 47SBCh. 1.1 - Prob. 48SBCh. 1.1 - Prob. 49SBCh. 1.1 - Prob. 50SBCh. 1.1 - Prob. 51SBCh. 1.1 - Prob. 52SBCh. 1.1 - Prob. 53SBCh. 1.1 - Prob. 54SBCh. 1.1 - Prob. 55SBCh. 1.1 - Prob. 56SBCh. 1.1 - Prob. 57SBCh. 1.1 - Prob. 58SBCh. 1.1 - Prob. 59SBCh. 1.1 - Prob. 60SBCh. 1.1 - Prob. 61SBCh. 1.1 - Prob. 62SBCh. 1.1 - Prob. 63SBCh. 1.1 - Prob. 64SBCh. 1.1 - Prob. 65SBCh. 1.1 - Prob. 66SBCh. 1.1 - Prob. 67SBCh. 1.1 - Prob. 68SBCh. 1.1 - Prob. 69SBCh. 1.1 - Prob. 70SBCh. 1.1 - Prob. 71AECh. 1.1 - Prob. 72AECh. 1.1 - Prob. 73AECh. 1.1 - Prob. 74AECh. 1.1 - Prob. 75AECh. 1.1 - Prob. 76AECh. 1.1 - Prob. 77AECh. 1.1 - Prob. 78AECh. 1.1 - Prob. 79AECh. 1.1 - Prob. 80AECh. 1.1 - Prob. 81AECh. 1.1 - Prob. 82AECh. 1.1 - Prob. 83AECh. 1.1 - Prob. 84AECh. 1.1 - Prob. 85AECh. 1.1 - Prob. 86AECh. 1.1 - Prob. 87AECh. 1.1 - Prob. 88AECh. 1.1 - Prob. 89AECh. 1.1 - Prob. 90AECh. 1.1 - Prob. 91AECh. 1.1 - Prob. 92AECh. 1.1 - Prob. 93AECh. 1.1 - Prob. 94AECh. 1.1 - Prob. 95AECh. 1.1 - Prob. 96AECh. 1.1 - Prob. 97AECh. 1.1 - Prob. 98AECh. 1.1 - Prob. 99AECh. 1.1 - Prob. 100DWCh. 1.1 - Prob. 101DWCh. 1.1 - Prob. 102DWCh. 1.2 - Prob. 1AYPCh. 1.2 - Prob. 2AYPCh. 1.2 - Prob. 3AYPCh. 1.2 - Prob. 4AYPCh. 1.2 - Prob. 5AYPCh. 1.2 - Prob. 6CVCh. 1.2 - Prob. 7CVCh. 1.2 - Prob. 8CVCh. 1.2 - Prob. 9CVCh. 1.2 - Prob. 10CVCh. 1.2 - Prob. 11SBCh. 1.2 - Prob. 12SBCh. 1.2 - Prob. 13SBCh. 1.2 - Prob. 14SBCh. 1.2 - Prob. 15SBCh. 1.2 - Prob. 16SBCh. 1.2 - Prob. 17SBCh. 1.2 - Prob. 18SBCh. 1.2 - Prob. 19SBCh. 1.2 - Prob. 20SBCh. 1.2 - Prob. 21SBCh. 1.2 - Prob. 22SBCh. 1.2 - Prob. 23SBCh. 1.2 - Prob. 24SBCh. 1.2 - Prob. 25SBCh. 1.2 - Prob. 26SBCh. 1.2 - Prob. 27SBCh. 1.2 - Prob. 28SBCh. 1.2 - Prob. 29SBCh. 1.2 - Prob. 30SBCh. 1.2 - Prob. 31SBCh. 1.2 - Prob. 32SBCh. 1.2 - Prob. 33SBCh. 1.2 - Prob. 34SBCh. 1.2 - Prob. 35SBCh. 1.2 - Prob. 36SBCh. 1.2 - Prob. 37SBCh. 1.2 - Prob. 38SBCh. 1.2 - Prob. 39SBCh. 1.2 - Prob. 40SBCh. 1.2 - Prob. 41SBCh. 1.2 - Prob. 42SBCh. 1.2 - Prob. 43SBCh. 1.2 - Prob. 44SBCh. 1.2 - Prob. 45SBCh. 1.2 - Prob. 46SBCh. 1.2 - Prob. 47SBCh. 1.2 - Prob. 48SBCh. 1.2 - Prob. 49SBCh. 1.2 - Prob. 50SBCh. 1.2 - Prob. 51SBCh. 1.2 - Prob. 52SBCh. 1.2 - Prob. 53SBCh. 1.2 - Prob. 54SBCh. 1.2 - Prob. 55SBCh. 1.2 - Prob. 56SBCh. 1.2 - Prob. 57SBCh. 1.2 - Prob. 58SBCh. 1.2 - Prob. 59SBCh. 1.2 - Prob. 60SBCh. 1.2 - Prob. 61SBCh. 1.2 - Prob. 62SBCh. 1.2 - Prob. 63SBCh. 1.2 - Prob. 64SBCh. 1.2 - Prob. 65SBCh. 1.2 - Prob. 66SBCh. 1.2 - Prob. 67SBCh. 1.2 - Prob. 68SBCh. 1.2 - Prob. 69SBCh. 1.2 - Prob. 70SBCh. 1.2 - Prob. 71SBCh. 1.2 - Prob. 72SBCh. 1.2 - Prob. 73SBCh. 1.2 - Prob. 74SBCh. 1.2 - Prob. 75SBCh. 1.2 - Prob. 76SBCh. 1.2 - Prob. 77SBCh. 1.2 - Prob. 78SBCh. 1.2 - Prob. 79MPCh. 1.2 - Prob. 80MPCh. 1.2 - Prob. 81MPCh. 1.2 - Prob. 82MPCh. 1.2 - Prob. 83MPCh. 1.2 - Prob. 84MPCh. 1.2 - Prob. 85MPCh. 1.2 - Prob. 86MPCh. 1.2 - Prob. 87MPCh. 1.2 - Prob. 88MPCh. 1.2 - Prob. 89MPCh. 1.2 - Prob. 90MPCh. 1.2 - Prob. 91MPCh. 1.2 - Prob. 92MPCh. 1.2 - Prob. 93AECh. 1.2 - Prob. 94AECh. 1.2 - Prob. 95AECh. 1.2 - Prob. 96AECh. 1.2 - Prob. 97AECh. 1.2 - Prob. 98AECh. 1.2 - Prob. 99AECh. 1.2 - Prob. 100AECh. 1.2 - Prob. 101AECh. 1.2 - Prob. 102AECh. 1.2 - Prob. 103AECh. 1.2 - Prob. 104AECh. 1.2 - Prob. 105AECh. 1.2 - Prob. 106AECh. 1.2 - Prob. 107AECh. 1.2 - Prob. 108AECh. 1.2 - Prob. 109AECh. 1.2 - Prob. 110AECh. 1.2 - Prob. 111AECh. 1.2 - Prob. 112AECh. 1.2 - Prob. 113AECh. 1.2 - Prob. 114AECh. 1.2 - Prob. 115AECh. 1.2 - Prob. 116AECh. 1.2 - Prob. 117AECh. 1.2 - Prob. 118AECh. 1.2 - Prob. 119AECh. 1.2 - Prob. 120AECh. 1.2 - Prob. 121AECh. 1.2 - Prob. 122AECh. 1.2 - Prob. 123DWCh. 1.2 - Prob. 124DWCh. 1.2 - Prob. 125DWCh. 1.2 - Prob. 126DWCh. 1.2 - Prob. 127DWCh. 1.3 - Prob. 1AYPCh. 1.3 - Prob. 2AYPCh. 1.3 - Prob. 3AYPCh. 1.3 - Prob. 4CVCh. 1.3 - Prob. 5CVCh. 1.3 - Prob. 6CVCh. 1.3 - Prob. 7CVCh. 1.3 - Prob. 8CVCh. 1.3 - Prob. 9CVCh. 1.3 - Prob. 10CVCh. 1.3 - Prob. 11SBCh. 1.3 - Prob. 12SBCh. 1.3 - Prob. 13SBCh. 1.3 - Prob. 14SBCh. 1.3 - Prob. 15SBCh. 1.3 - Prob. 16SBCh. 1.3 - Prob. 17SBCh. 1.3 - Prob. 18SBCh. 1.3 - Prob. 19SBCh. 1.3 - Prob. 20SBCh. 1.3 - Prob. 21SBCh. 1.3 - Prob. 22SBCh. 1.3 - Prob. 23SBCh. 1.3 - Prob. 24SBCh. 1.3 - Prob. 25SBCh. 1.3 - Prob. 26SBCh. 1.3 - Prob. 27SBCh. 1.3 - Prob. 28SBCh. 1.3 - Prob. 29SBCh. 1.3 - Prob. 30SBCh. 1.3 - Prob. 31SBCh. 1.3 - Prob. 32SBCh. 1.3 - Prob. 33SBCh. 1.3 - Prob. 34SBCh. 1.3 - Prob. 35SBCh. 1.3 - Prob. 36SBCh. 1.3 - Prob. 37SBCh. 1.3 - Prob. 38SBCh. 1.3 - Prob. 39SBCh. 1.3 - Prob. 40SBCh. 1.3 - Prob. 41SBCh. 1.3 - Prob. 42SBCh. 1.3 - Prob. 43SBCh. 1.3 - Prob. 44SBCh. 1.3 - Prob. 45SBCh. 1.3 - Prob. 46SBCh. 1.3 - Prob. 47SBCh. 1.3 - Prob. 48SBCh. 1.3 - Prob. 49SBCh. 1.3 - Prob. 50SBCh. 1.3 - Prob. 51SBCh. 1.3 - Prob. 52SBCh. 1.3 - Prob. 53SBCh. 1.3 - Prob. 54SBCh. 1.3 - Prob. 55SBCh. 1.3 - Prob. 56SBCh. 1.3 - Prob. 57SBCh. 1.3 - Prob. 58SBCh. 1.3 - Prob. 59SBCh. 1.3 - Prob. 60SBCh. 1.3 - Prob. 61SBCh. 1.3 - Prob. 62SBCh. 1.3 - Prob. 63SBCh. 1.3 - Prob. 64SBCh. 1.3 - Prob. 65SBCh. 1.3 - Prob. 66SBCh. 1.3 - Prob. 67SBCh. 1.3 - Prob. 68SBCh. 1.3 - Prob. 69SBCh. 1.3 - Prob. 70SBCh. 1.3 - Prob. 71SBCh. 1.3 - Prob. 72SBCh. 1.3 - Prob. 73SBCh. 1.3 - Prob. 74SBCh. 1.3 - Prob. 75SBCh. 1.3 - Prob. 76SBCh. 1.3 - Prob. 77SBCh. 1.3 - Prob. 78SBCh. 1.3 - Prob. 79SBCh. 1.3 - Prob. 80SBCh. 1.3 - Prob. 81SBCh. 1.3 - Prob. 82SBCh. 1.3 - Prob. 83SBCh. 1.3 - Prob. 84SBCh. 1.3 - Prob. 85SBCh. 1.3 - Prob. 86SBCh. 1.3 - Prob. 87AECh. 1.3 - Prob. 88AECh. 1.3 - Prob. 89AECh. 1.3 - Prob. 90AECh. 1.3 - Prob. 91AECh. 1.3 - Prob. 92AECh. 1.3 - Prob. 93DWCh. 1.3 - Prob. 94DWCh. 1.3 - Prob. 95DWCh. 1.3 - Prob. 96DWCh. 1.3 - Prob. 97DWCh. 1.4 - Prob. 1AYPCh. 1.4 - Prob. 2AYPCh. 1.4 - Prob. 3AYPCh. 1.4 - Prob. 4CVCh. 1.4 - Prob. 5CVCh. 1.4 - Prob. 6CVCh. 1.4 - Prob. 7CVCh. 1.4 - Prob. 8CVCh. 1.4 - Prob. 9SBCh. 1.4 - Prob. 10SBCh. 1.4 - Prob. 11SBCh. 1.4 - Prob. 12SBCh. 1.4 - Prob. 13SBCh. 1.4 - Prob. 14SBCh. 1.4 - Prob. 15SBCh. 1.4 - Prob. 16SBCh. 1.4 - Prob. 17SBCh. 1.4 - Prob. 18SBCh. 1.4 - Prob. 19SBCh. 1.4 - Prob. 20SBCh. 1.4 - Prob. 21SBCh. 1.4 - Prob. 22SBCh. 1.4 - Prob. 23SBCh. 1.4 - Prob. 24SBCh. 1.4 - Prob. 25SBCh. 1.4 - Prob. 26SBCh. 1.4 - Prob. 27SBCh. 1.4 - Prob. 28SBCh. 1.4 - Prob. 29SBCh. 1.4 - Prob. 30SBCh. 1.4 - Prob. 31SBCh. 1.4 - Prob. 32SBCh. 1.4 - Prob. 33SBCh. 1.4 - Prob. 34SBCh. 1.4 - Prob. 35SBCh. 1.4 - Prob. 36SBCh. 1.4 - Prob. 37SBCh. 1.4 - Prob. 38SBCh. 1.4 - Prob. 39SBCh. 1.4 - Prob. 40SBCh. 1.4 - Prob. 41SBCh. 1.4 - Prob. 42SBCh. 1.4 - Prob. 43SBCh. 1.4 - Prob. 44SBCh. 1.4 - Prob. 45SBCh. 1.4 - Prob. 46SBCh. 1.4 - Prob. 47SBCh. 1.4 - Prob. 48SBCh. 1.4 - Prob. 49SBCh. 1.4 - Prob. 50SBCh. 1.4 - Prob. 51SBCh. 1.4 - Prob. 52SBCh. 1.4 - Prob. 53SBCh. 1.4 - Prob. 54SBCh. 1.4 - Prob. 55SBCh. 1.4 - Prob. 56SBCh. 1.4 - Prob. 57SBCh. 1.4 - Prob. 58SBCh. 1.4 - Prob. 59SBCh. 1.4 - Prob. 60SBCh. 1.4 - Prob. 61SBCh. 1.4 - Prob. 62SBCh. 1.4 - Prob. 63SBCh. 1.4 - Prob. 64SBCh. 1.4 - Prob. 65SBCh. 1.4 - Prob. 66SBCh. 1.4 - Prob. 67SBCh. 1.4 - Prob. 68SBCh. 1.4 - Prob. 69SBCh. 1.4 - Prob. 70SBCh. 1.4 - Prob. 71SBCh. 1.4 - Prob. 72SBCh. 1.4 - Prob. 73SBCh. 1.4 - Prob. 74SBCh. 1.4 - Prob. 75SBCh. 1.4 - Prob. 76SBCh. 1.4 - Prob. 77SBCh. 1.4 - Prob. 78SBCh. 1.4 - Prob. 79SBCh. 1.4 - Prob. 80SBCh. 1.4 - Prob. 81SBCh. 1.4 - Prob. 82SBCh. 1.4 - Prob. 83SBCh. 1.4 - Prob. 84SBCh. 1.4 - Prob. 85SBCh. 1.4 - Prob. 86SBCh. 1.4 - Prob. 87SBCh. 1.4 - Prob. 88SBCh. 1.4 - Prob. 89SBCh. 1.4 - Prob. 90SBCh. 1.4 - Prob. 91SBCh. 1.4 - Prob. 92SBCh. 1.4 - Prob. 93SBCh. 1.4 - Prob. 94SBCh. 1.4 - Prob. 95SBCh. 1.4 - Prob. 96SBCh. 1.4 - Prob. 97MPCh. 1.4 - Prob. 98MPCh. 1.4 - Prob. 99APPCh. 1.4 - Prob. 100APPCh. 1.4 - Prob. 101APPCh. 1.4 - Prob. 102DWCh. 1.4 - Prob. 103DWCh. 1.4 - Prob. 104DWCh. 1.4 - Prob. 105DWCh. 1.5 - Prob. 1AYPCh. 1.5 - Prob. 2AYPCh. 1.5 - Prob. 3CVCh. 1.5 - Prob. 4CVCh. 1.5 - Prob. 5CVCh. 1.5 - Prob. 6CVCh. 1.5 - Prob. 7CVCh. 1.5 - Prob. 8CVCh. 1.5 - Prob. 9CVCh. 1.5 - Prob. 10CVCh. 1.5 - Prob. 11CVCh. 1.5 - Prob. 12CVCh. 1.5 - Prob. 13SBCh. 1.5 - Prob. 14SBCh. 1.5 - Prob. 15SBCh. 1.5 - Prob. 16SBCh. 1.5 - Prob. 17SBCh. 1.5 - Prob. 18SBCh. 1.5 - Prob. 19SBCh. 1.5 - Prob. 20SBCh. 1.5 - Prob. 21SBCh. 1.5 - Prob. 22SBCh. 1.5 - Prob. 23SBCh. 1.5 - Prob. 24SBCh. 1.5 - Prob. 25SBCh. 1.5 - Prob. 26SBCh. 1.5 - Prob. 27SBCh. 1.5 - Prob. 28SBCh. 1.5 - Prob. 29SBCh. 1.5 - Prob. 30SBCh. 1.5 - Prob. 31SBCh. 1.5 - Prob. 32SBCh. 1.5 - Prob. 33SBCh. 1.5 - Prob. 34SBCh. 1.5 - Prob. 35SBCh. 1.5 - Prob. 36SBCh. 1.5 - Prob. 37SBCh. 1.5 - Prob. 38SBCh. 1.5 - Prob. 39SBCh. 1.5 - Prob. 40SBCh. 1.5 - Prob. 41SBCh. 1.5 - Prob. 42SBCh. 1.5 - Prob. 43SBCh. 1.5 - Prob. 44SBCh. 1.5 - Prob. 45SBCh. 1.5 - Prob. 46SBCh. 1.5 - Prob. 47SBCh. 1.5 - Prob. 48SBCh. 1.5 - Prob. 49SBCh. 1.5 - Prob. 50SBCh. 1.5 - Prob. 51SBCh. 1.5 - Prob. 52SBCh. 1.5 - Prob. 53SBCh. 1.5 - Prob. 54SBCh. 1.5 - Prob. 55SBCh. 1.5 - Prob. 56SBCh. 1.5 - Prob. 57SBCh. 1.5 - Prob. 58SBCh. 1.5 - Prob. 59SBCh. 1.5 - Prob. 60SBCh. 1.5 - Prob. 61SBCh. 1.5 - Prob. 62SBCh. 1.5 - Prob. 63SBCh. 1.5 - Prob. 64SBCh. 1.5 - Prob. 65SBCh. 1.5 - Prob. 66SBCh. 1.5 - Prob. 67SBCh. 1.5 - Prob. 68SBCh. 1.5 - Prob. 69SBCh. 1.5 - Prob. 70SBCh. 1.5 - Prob. 71SBCh. 1.5 - Prob. 72SBCh. 1.5 - Prob. 73SBCh. 1.5 - Prob. 74SBCh. 1.5 - Prob. 75SBCh. 1.5 - Prob. 76SBCh. 1.5 - Prob. 77SBCh. 1.5 - Prob. 78SBCh. 1.5 - Prob. 79SBCh. 1.5 - Prob. 80SBCh. 1.5 - Prob. 81SBCh. 1.5 - Prob. 82SBCh. 1.5 - Prob. 83SBCh. 1.5 - Prob. 84SBCh. 1.5 - Prob. 85SBCh. 1.5 - Prob. 86SBCh. 1.5 - Prob. 87SBCh. 1.5 - Prob. 88SBCh. 1.5 - Prob. 89SBCh. 1.5 - Prob. 90SBCh. 1.5 - Prob. 91SBCh. 1.5 - Prob. 92SBCh. 1.5 - Prob. 93AECh. 1.5 - Prob. 94AECh. 1.5 - Prob. 95AECh. 1.5 - Prob. 96AECh. 1.5 - Prob. 97AECh. 1.5 - Prob. 98AECh. 1.5 - Prob. 99AECh. 1.5 - Prob. 100AECh. 1.5 - Prob. 101AECh. 1.5 - Prob. 102AECh. 1.5 - Prob. 103AECh. 1.5 - Prob. 104AECh. 1.5 - Prob. 105AECh. 1.5 - Prob. 106AECh. 1.5 - Prob. 107AECh. 1.5 - Prob. 108AECh. 1.5 - Prob. 109AECh. 1.5 - Prob. 110AECh. 1.5 - Prob. 111AECh. 1.5 - Prob. 112AECh. 1.5 - Prob. 113AECh. 1.5 - Prob. 114AECh. 1.5 - Prob. 115AECh. 1.5 - Prob. 116AECh. 1.5 - Prob. 117AECh. 1.5 - Prob. 118AECh. 1.5 - Prob. 119AECh. 1.5 - Prob. 120AECh. 1.5 - Prob. 121AECh. 1.5 - Prob. 122AECh. 1.5 - Prob. 123AECh. 1.5 - Prob. 124AECh. 1.5 - Prob. 125AECh. 1.5 - Prob. 126DWCh. 1.5 - Prob. 127DWCh. 1.5 - Prob. 128DWCh. 1.5 - Prob. 129DWCh. 1.6 - Prob. 1AYPCh. 1.6 - Prob. 2AYPCh. 1.6 - Prob. 3CVCh. 1.6 - Prob. 4CVCh. 1.6 - Prob. 5CVCh. 1.6 - Prob. 6CVCh. 1.6 - Prob. 7CVCh. 1.6 - Prob. 8CVCh. 1.6 - Prob. 9SBCh. 1.6 - Prob. 10SBCh. 1.6 - Prob. 11SBCh. 1.6 - Prob. 12SBCh. 1.6 - Prob. 13SBCh. 1.6 - Prob. 14SBCh. 1.6 - Prob. 15SBCh. 1.6 - Prob. 16SBCh. 1.6 - Prob. 17SBCh. 1.6 - Prob. 18SBCh. 1.6 - Prob. 19SBCh. 1.6 - Prob. 20SBCh. 1.6 - Prob. 21SBCh. 1.6 - Prob. 22SBCh. 1.6 - Prob. 23SBCh. 1.6 - Prob. 24SBCh. 1.6 - Prob. 25SBCh. 1.6 - Prob. 26SBCh. 1.6 - Prob. 27SBCh. 1.6 - Prob. 28SBCh. 1.6 - Prob. 29SBCh. 1.6 - Prob. 30SBCh. 1.6 - Prob. 31SBCh. 1.6 - Prob. 32SBCh. 1.6 - Prob. 33SBCh. 1.6 - Prob. 34SBCh. 1.6 - Prob. 35SBCh. 1.6 - Prob. 36SBCh. 1.6 - Prob. 37SBCh. 1.6 - Prob. 38SBCh. 1.6 - Prob. 39SBCh. 1.6 - Prob. 40SBCh. 1.6 - Prob. 41SBCh. 1.6 - Prob. 42SBCh. 1.6 - Prob. 43SBCh. 1.6 - Prob. 44SBCh. 1.6 - Prob. 45SBCh. 1.6 - Prob. 46SBCh. 1.6 - Prob. 47SBCh. 1.6 - Prob. 48SBCh. 1.6 - Prob. 49SBCh. 1.6 - Prob. 50SBCh. 1.6 - Prob. 51SBCh. 1.6 - Prob. 52SBCh. 1.6 - Prob. 53SBCh. 1.6 - Prob. 54SBCh. 1.6 - Prob. 55SBCh. 1.6 - Prob. 56SBCh. 1.6 - Prob. 57SBCh. 1.6 - Prob. 58SBCh. 1.6 - Prob. 59SBCh. 1.6 - Prob. 60SBCh. 1.6 - Prob. 61SBCh. 1.6 - Prob. 62SBCh. 1.6 - Prob. 63SBCh. 1.6 - Prob. 64SBCh. 1.6 - Prob. 65AECh. 1.6 - Prob. 66AECh. 1.6 - Prob. 67AECh. 1.6 - Prob. 68AECh. 1.6 - Prob. 69AECh. 1.6 - Prob. 70AECh. 1.6 - Prob. 71AECh. 1.6 - Prob. 72AECh. 1.6 - Prob. 73AECh. 1.6 - Prob. 74AECh. 1.6 - Prob. 75AECh. 1.6 - Prob. 76AECh. 1.6 - Prob. 77AECh. 1.6 - Prob. 78AECh. 1.6 - Prob. 79AECh. 1.6 - Prob. 80AECh. 1.6 - Prob. 81AECh. 1.6 - Prob. 82AECh. 1.6 - Prob. 83AECh. 1.6 - Prob. 84AECh. 1.6 - Prob. 85AECh. 1.6 - Prob. 86AECh. 1.6 - Prob. 87AECh. 1.6 - Prob. 88AECh. 1.6 - Prob. 89AECh. 1.6 - Prob. 90AECh. 1.6 - Prob. 91AECh. 1.6 - Prob. 92AECh. 1.6 - Prob. 93AECh. 1.6 - Prob. 94AECh. 1.6 - Prob. 95DWCh. 1.6 - Prob. 96DWCh. 1.6 - Prob. 97DWCh. 1.7 - Prob. 1CVCh. 1.7 - Prob. 2CVCh. 1.7 - Prob. 3CVCh. 1.7 - Prob. 4CVCh. 1.7 - Prob. 5CVCh. 1.7 - Prob. 6CVCh. 1.7 - Prob. 7CVCh. 1.7 - Prob. 8CVCh. 1.7 - Prob. 9AECh. 1.7 - Prob. 10AECh. 1.7 - Prob. 11AECh. 1.7 - Prob. 12AECh. 1.7 - Prob. 13AECh. 1.7 - Prob. 14AECh. 1.7 - Prob. 15AECh. 1.7 - Prob. 16AECh. 1.7 - Prob. 17AECh. 1.7 - Prob. 18AECh. 1.7 - Prob. 19AECh. 1.7 - Prob. 20AECh. 1.7 - Prob. 21AECh. 1.7 - Prob. 22AECh. 1.7 - Prob. 23AECh. 1.7 - Prob. 24AECh. 1.7 - Prob. 25AECh. 1.7 - Prob. 26AECh. 1.7 - Prob. 27AECh. 1.7 - Prob. 28AECh. 1.7 - Prob. 29AECh. 1.7 - Prob. 30AECh. 1.7 - Prob. 31AECh. 1.7 - Prob. 32AECh. 1.7 - Prob. 33AECh. 1.7 - Prob. 34AECh. 1.7 - Prob. 35AECh. 1.7 - Prob. 36AECh. 1.7 - Prob. 37AECh. 1.7 - Prob. 38AECh. 1.7 - Prob. 39AECh. 1.7 - Prob. 40AECh. 1.7 - Prob. 41AECh. 1.7 - Prob. 42AECh. 1.7 - Prob. 43AECh. 1.7 - Prob. 44AECh. 1.7 - Prob. 45AECh. 1.7 - Prob. 46AECh. 1.7 - Prob. 47AECh. 1.7 - Prob. 48AECh. 1.7 - Prob. 49AECh. 1.7 - Prob. 50AECh. 1.7 - Prob. 51AECh. 1.7 - Prob. 52AECh. 1.7 - Prob. 53AECh. 1.7 - Prob. 54AECh. 1.7 - Prob. 55AECh. 1.7 - Prob. 56AECh. 1.7 - Prob. 57DWCh. 1.7 - Prob. 58DWCh. 1.7 - Prob. 59DWCh. 1.7 - Prob. 60DWCh. 1.7 - Prob. 61DW
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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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