EBK ALGEBRA FOUNDATIONS
15th Edition
ISBN: 9780321978929
Author: Martin-Gay
Publisher: PEARSON
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Chapter 15.1, Problem 8ES
Objetive A Graph each linear function. See Example 1 and 2.
8.
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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 15 Solutions
EBK ALGEBRA FOUNDATIONS
Ch. 15.1 - Use the choices given to fill in each blank. Not...Ch. 15.1 - Prob. 2VRVCCh. 15.1 - Prob. 3VRVCCh. 15.1 - State the slope and the y-intercept of the graph...Ch. 15.1 - Prob. 5VRVCCh. 15.1 - Prob. 6VRVCCh. 15.1 - Prob. 7VRVCCh. 15.1 - Prob. 8VRVCCh. 15.1 - Prob. 9VRVCCh. 15.1 - Prob. 10VRVC
Ch. 15.1 - Prob. 1ESCh. 15.1 - Prob. 2ESCh. 15.1 - Prob. 3ESCh. 15.1 - Prob. 4ESCh. 15.1 - Prob. 5ESCh. 15.1 - Prob. 6ESCh. 15.1 - Prob. 7ESCh. 15.1 - Objetive A Graph each linear function. See Example...Ch. 15.1 - Prob. 9ESCh. 15.1 - Prob. 10ESCh. 15.1 - Prob. 11ESCh. 15.1 - Prob. 12ESCh. 15.1 - Prob. 13ESCh. 15.1 - Prob. 14ESCh. 15.1 - Prob. 15ESCh. 15.1 - Prob. 16ESCh. 15.1 - Prob. 17ESCh. 15.1 - Prob. 18ESCh. 15.1 - Prob. 19ESCh. 15.1 - Prob. 20ESCh. 15.1 - Prob. 21ESCh. 15.1 - Prob. 22ESCh. 15.1 - Prob. 23ESCh. 15.1 - Prob. 24ESCh. 15.1 - Prob. 25ESCh. 15.1 - Prob. 26ESCh. 15.1 - Prob. 27ESCh. 15.1 - Prob. 28ESCh. 15.1 - Prob. 29ESCh. 15.1 - Prob. 30ESCh. 15.1 - Prob. 31ESCh. 15.1 - Prob. 32ESCh. 15.1 - Find an equation of the line passing through the...Ch. 15.1 - Prob. 34ESCh. 15.1 - Prob. 35ESCh. 15.1 - Prob. 36ESCh. 15.1 - Prob. 37ESCh. 15.1 - Prob. 38ESCh. 15.1 - Prob. 39ESCh. 15.1 - Prob. 40ESCh. 15.1 - Prob. 41ESCh. 15.1 - Prob. 42ESCh. 15.1 - Prob. 43ESCh. 15.1 - Prob. 44ESCh. 15.1 - Prob. 45ESCh. 15.1 - Prob. 46ESCh. 15.1 - Prob. 47ESCh. 15.1 - Prob. 48ESCh. 15.1 - Prob. 49ESCh. 15.1 - Prob. 50ESCh. 15.1 - Prob. 51ESCh. 15.1 - Prob. 52ESCh. 15.1 - Prob. 53ESCh. 15.1 - Objective B C Mixed Practice Find an equation of...Ch. 15.1 - Prob. 55ESCh. 15.1 - Prob. 56ESCh. 15.1 - Prob. 57ESCh. 15.1 - Prob. 58ESCh. 15.1 - Prob. 59ESCh. 15.1 - Prob. 60ESCh. 15.1 - Prob. 61ESCh. 15.1 - Prob. 62ESCh. 15.1 - Prob. 63ESCh. 15.1 - Prob. 64ESCh. 15.1 - Prob. 65ESCh. 15.1 - Prob. 66ESCh. 15.1 - Prob. 67ESCh. 15.1 - Prob. 68ESCh. 15.1 - Prob. 69ESCh. 15.1 - Prob. 70ESCh. 15.1 - Prob. 71ESCh. 15.1 - Prob. 72ESCh. 15.1 - Prob. 73ESCh. 15.1 - Prob. 74ESCh. 15.1 - Prob. 75ESCh. 15.1 - Prob. 76ESCh. 15.1 - Prob. 77ESCh. 15.1 - Prob. 78ESCh. 15.1 - Prob. 79ESCh. 15.1 - Prob. 80ESCh. 15.1 - Prob. 81ESCh. 15.1 - Prob. 82ESCh. 15.1 - Prob. 83ESCh. 15.1 - Prob. 84ESCh. 15.1 - Prob. 85ESCh. 15.1 - Prob. 86ESCh. 15.1 - Prob. 87ESCh. 15.1 - Prob. 88ESCh. 15.1 - Prob. 89ESCh. 15.1 - Prob. 90ESCh. 15.1 - Find an equation of the perpendicular bisector of...Ch. 15.1 - Prob. 92ESCh. 15.1 - Solve. 93. Describe how to check to see if the...Ch. 15.2 - Prob. 1VRVCCh. 15.2 - Prob. 2VRVCCh. 15.2 - Prob. 3VRVCCh. 15.2 - Prob. 4VRVCCh. 15.2 - Prob. 1ESCh. 15.2 - Prob. 2ESCh. 15.2 - Prob. 3ESCh. 15.2 - Prob. 4ESCh. 15.2 - Prob. 5ESCh. 15.2 - Prob. 6ESCh. 15.2 - Prob. 7ESCh. 15.2 - Prob. 8ESCh. 15.2 - Prob. 9ESCh. 15.2 - Prob. 10ESCh. 15.2 - Prob. 11ESCh. 15.2 - Prob. 12ESCh. 15.2 - Prob. 13ESCh. 15.2 - Prob. 14ESCh. 15.2 - Prob. 15ESCh. 15.2 - Prob. 16ESCh. 15.2 - Prob. 17ESCh. 15.2 - Prob. 18ESCh. 15.2 - Prob. 19ESCh. 15.2 - Prob. 20ESCh. 15.2 - Prob. 21ESCh. 15.2 - Prob. 22ESCh. 15.2 - Prob. 23ESCh. 15.2 - Prob. 24ESCh. 15.2 - Prob. 25ESCh. 15.2 - Prob. 26ESCh. 15.2 - Prob. 27ESCh. 15.2 - Prob. 28ESCh. 15.2 - Prob. 29ESCh. 15.2 - Prob. 30ESCh. 15.2 - Prob. 31ESCh. 15.2 - Prob. 32ESCh. 15.2 - Prob. 33ESCh. 15.2 - Prob. 34ESCh. 15.2 - Prob. 35ESCh. 15.2 - Prob. 36ESCh. 15.2 - Prob. 37ESCh. 15.2 - Prob. 38ESCh. 15.2 - Prob. 39ESCh. 15.2 - Prob. 40ESCh. 15.2 - Prob. 41ESCh. 15.2 - Prob. 42ESCh. 15.2 - Prob. 43ESCh. 15.2 - Prob. 44ESCh. 15.2 - Prob. 45ESCh. 15.2 - Prob. 46ESCh. 15.2 - Prob. 47ESCh. 15.2 - Prob. 48ESCh. 15.2 - Prob. 49ESCh. 15.2 - Prob. 50ESCh. 15.2 - Forensic scientists use the following functions to...Ch. 15.2 - Prob. 52ESCh. 15.2 - Prob. 53ESCh. 15.2 - Prob. 54ESCh. 15.2 - Prob. 55ESCh. 15.2 - Prob. 56ESCh. 15.2 - Prob. 57ESCh. 15.2 - Prob. 58ESCh. 15.2 - Prob. 59ESCh. 15.2 - Prob. 60ESCh. 15.2 - Prob. 61ESCh. 15.2 - Prob. 62ESCh. 15.2 - Prob. 63ESCh. 15.2 - Prob. 64ESCh. 15.2 - Prob. 65ESCh. 15.2 - Prob. 66ESCh. 15.2 - Prob. 67ESCh. 15.2 - Prob. 68ESCh. 15.2 - Graph y=x24x+7. Let x=0,1,2,3,4 to generate...Ch. 15.2 - Graph y=x2+2x+3. Let x=3,2,1,0,1 to generate...Ch. 15.2 - Prob. 71ESCh. 15.3 - Prob. 1VRVCCh. 15.3 - Prob. 2VRVCCh. 15.3 - Prob. 3VRVCCh. 15.3 - Prob. 4VRVCCh. 15.3 - Prob. 1ESCh. 15.3 - Prob. 2ESCh. 15.3 - Prob. 3ESCh. 15.3 - Prob. 4ESCh. 15.3 - Prob. 5ESCh. 15.3 - Prob. 6ESCh. 15.3 - Prob. 7ESCh. 15.3 - Prob. 8ESCh. 15.3 - Prob. 9ESCh. 15.3 - Prob. 10ESCh. 15.3 - Prob. 11ESCh. 15.3 - Prob. 12ESCh. 15.3 - Prob. 13ESCh. 15.3 - Prob. 14ESCh. 15.3 - Prob. 15ESCh. 15.3 - Prob. 16ESCh. 15.3 - Prob. 17ESCh. 15.3 - Prob. 18ESCh. 15.3 - Prob. 19ESCh. 15.3 - Prob. 20ESCh. 15.3 - Prob. 21ESCh. 15.3 - Prob. 22ESCh. 15.3 - Prob. 23ESCh. 15.3 - Prob. 24ESCh. 15.3 - Prob. 25ESCh. 15.3 - Prob. 26ESCh. 15.3 - Prob. 27ESCh. 15.3 - Prob. 28ESCh. 15.3 - Prob. 29ESCh. 15.3 - Prob. 30ESCh. 15.3 - Prob. 31ESCh. 15.3 - Prob. 32ESCh. 15.3 - Prob. 33ESCh. 15.3 - Prob. 34ESCh. 15.3 - Prob. 35ESCh. 15.3 - Prob. 36ESCh. 15.3 - Prob. 37ESCh. 15.3 - Prob. 38ESCh. 15.3 - Prob. 39ESCh. 15.3 - Prob. 40ESCh. 15.3 - Prob. 41ESCh. 15.3 - Prob. 42ESCh. 15.3 - Prob. 43ESCh. 15.3 - Prob. 44ESCh. 15.3 - Prob. 45ESCh. 15.3 - Prob. 46ESCh. 15.3 - Prob. 47ESCh. 15.3 - Prob. 48ESCh. 15.3 - Prob. 49ESCh. 15.3 - Prob. 50ESCh. 15.3 - Prob. 51ESCh. 15.3 - Prob. 52ESCh. 15.3 - Prob. 53ESCh. 15.3 - Prob. 54ESCh. 15.3 - Prob. 55ESCh. 15.3 - Prob. 56ESCh. 15.3 - Prob. 57ESCh. 15.3 - Prob. 58ESCh. 15.3 - Prob. 59ESCh. 15.3 - Prob. 60ESCh. 15.3 - Prob. 61ESCh. 15.3 - Prob. 62ESCh. 15.3 - Prob. 63ESCh. 15.3 - Prob. 64ESCh. 15.3 - Prob. 65ESCh. 15.3 - Prob. 66ESCh. 15.3 - Prob. 67ESCh. 15.3 - Prob. 68ESCh. 15.3 - Prob. 69ESCh. 15.3 - Prob. 70ESCh. 15.4 - Prob. 1VRVCCh. 15.4 - Prob. 2VRVCCh. 15.4 - Prob. 3VRVCCh. 15.4 - Prob. 4VRVCCh. 15.4 - Prob. 5VRVCCh. 15.4 - Prob. 6VRVCCh. 15.4 - Prob. 7VRVCCh. 15.4 - Prob. 8VRVCCh. 15.4 - Prob. 1ESCh. 15.4 - Prob. 2ESCh. 15.4 - Prob. 3ESCh. 15.4 - Prob. 4ESCh. 15.4 - Prob. 5ESCh. 15.4 - Prob. 6ESCh. 15.4 - Prob. 7ESCh. 15.4 - Prob. 8ESCh. 15.4 - Prob. 9ESCh. 15.4 - Prob. 10ESCh. 15.4 - Prob. 11ESCh. 15.4 - Prob. 12ESCh. 15.4 - Prob. 13ESCh. 15.4 - Prob. 14ESCh. 15.4 - Prob. 15ESCh. 15.4 - Prob. 16ESCh. 15.4 - Prob. 17ESCh. 15.4 - Prob. 18ESCh. 15.4 - Prob. 19ESCh. 15.4 - Prob. 20ESCh. 15.4 - Prob. 21ESCh. 15.4 - Prob. 22ESCh. 15.4 - Prob. 23ESCh. 15.4 - Prob. 24ESCh. 15.4 - Prob. 25ESCh. 15.4 - Prob. 26ESCh. 15.4 - Prob. 27ESCh. 15.4 - Prob. 28ESCh. 15.4 - Prob. 29ESCh. 15.4 - Prob. 30ESCh. 15.4 - Prob. 31ESCh. 15.4 - Prob. 32ESCh. 15.4 - Prob. 33ESCh. 15.4 - Prob. 34ESCh. 15.4 - Prob. 35ESCh. 15.4 - Prob. 36ESCh. 15.4 - Prob. 37ESCh. 15.4 - Prob. 38ESCh. 15.4 - Objective D Solve. See Example 7. 39. The maximum...Ch. 15.4 - Objective D Solve. See Example 7. 40. The number...Ch. 15.4 - Prob. 41ESCh. 15.4 - Prob. 42ESCh. 15.4 - Prob. 43ESCh. 15.4 - Prob. 44ESCh. 15.4 - Prob. 45ESCh. 15.4 - Prob. 46ESCh. 15.4 - Prob. 47ESCh. 15.4 - Prob. 48ESCh. 15.4 - Prob. 49ESCh. 15.4 - Prob. 50ESCh. 15.4 - Prob. 51ESCh. 15.4 - Prob. 52ESCh. 15.4 - Prob. 53ESCh. 15.4 - Prob. 54ESCh. 15.4 - Prob. 55ESCh. 15.4 - Prob. 56ESCh. 15.4 - Prob. 57ESCh. 15.4 - Prob. 58ESCh. 15.4 - Prob. 59ESCh. 15.4 - Prob. 60ESCh. 15.4 - Prob. 61ESCh. 15.4 - Prob. 62ESCh. 15.4 - Prob. 63ESCh. 15.4 - Prob. 64ESCh. 15.4 - Prob. 65ESCh. 15.4 - Prob. 66ESCh. 15.4 - Prob. 67ESCh. 15.4 - Prob. 68ESCh. 15.4 - Prob. 69ESCh. 15.4 - Prob. 70ESCh. 15.4 - Prob. 71ESCh. 15.4 - Prob. 72ESCh. 15.4 - Prob. 73ESCh. 15.4 - Prob. 74ESCh. 15.4 - Prob. 75ESCh. 15.4 - Prob. 76ESCh. 15.4 - Prob. 77ESCh. 15.4 - Prob. 78ESCh. 15 - Prob. 1IRCh. 15 - Prob. 2IRCh. 15 - Prob. 3IRCh. 15 - Prob. 4IRCh. 15 - Prob. 5IRCh. 15 - Prob. 6IRCh. 15 - Prob. 7IRCh. 15 - Prob. 8IRCh. 15 - Prob. 9IRCh. 15 - Prob. 10IRCh. 15 - Prob. 11IRCh. 15 - Prob. 12IRCh. 15 - Prob. 13IRCh. 15 - Prob. 14IRCh. 15 - Prob. 15IRCh. 15 - Prob. 16IRCh. 15 - Prob. 17IRCh. 15 - Prob. 18IRCh. 15 - Prob. 19IRCh. 15 - Prob. 20IRCh. 15 - Prob. 21IRCh. 15 - Prob. 22IRCh. 15 - Prob. 23IRCh. 15 - Prob. 24IRCh. 15 - Prob. 25IRCh. 15 - Prob. 26IRCh. 15 - Prob. 1VCCh. 15 - Prob. 2VCCh. 15 - Prob. 3VCCh. 15 - Prob. 4VCCh. 15 - Prob. 5VCCh. 15 - Prob. 6VCCh. 15 - Prob. 7VCCh. 15 - Prob. 8VCCh. 15 - Prob. 9VCCh. 15 - Prob. 1RCh. 15 - Prob. 2RCh. 15 - Prob. 3RCh. 15 - Prob. 4RCh. 15 - Prob. 5RCh. 15 - Prob. 6RCh. 15 - Prob. 7RCh. 15 - Prob. 8RCh. 15 - Prob. 9RCh. 15 - Prob. 10RCh. 15 - Prob. 11RCh. 15 - Prob. 12RCh. 15 - Prob. 13RCh. 15 - Prob. 14RCh. 15 - Prob. 15RCh. 15 - Prob. 16RCh. 15 - Prob. 17RCh. 15 - Prob. 18RCh. 15 - Prob. 19RCh. 15 - Prob. 20RCh. 15 - Prob. 21RCh. 15 - Prob. 22RCh. 15 - Prob. 23RCh. 15 - Prob. 24RCh. 15 - Prob. 25RCh. 15 - Prob. 26RCh. 15 - Prob. 27RCh. 15 - Prob. 28RCh. 15 - Prob. 29RCh. 15 - Prob. 30RCh. 15 - Prob. 31RCh. 15 - Prob. 32RCh. 15 - Prob. 33RCh. 15 - Prob. 34RCh. 15 - Prob. 35RCh. 15 - Prob. 36RCh. 15 - Prob. 37RCh. 15 - Prob. 38RCh. 15 - Prob. 39RCh. 15 - Prob. 40RCh. 15 - Prob. 41RCh. 15 - Prob. 42RCh. 15 - Prob. 43RCh. 15 - Prob. 44RCh. 15 - Prob. 45RCh. 15 - Prob. 46RCh. 15 - Prob. 47RCh. 15 - Prob. 48RCh. 15 - Prob. 49RCh. 15 - Prob. 50RCh. 15 - Prob. 51RCh. 15 - Prob. 52RCh. 15 - Prob. 53RCh. 15 - Prob. 54RCh. 15 - Prob. 55RCh. 15 - Prob. 56RCh. 15 - Prob. 57RCh. 15 - Prob. 58RCh. 15 - Prob. 59RCh. 15 - Prob. 60RCh. 15 - Prob. 1TCh. 15 - Prob. 2TCh. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Prob. 6TCh. 15 - Prob. 7TCh. 15 - Prob. 8TCh. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - Prob. 12TCh. 15 - Prob. 13TCh. 15 - Prob. 14TCh. 15 - Prob. 15TCh. 15 - Prob. 16TCh. 15 - Prob. 17TCh. 15 - Prob. 18TCh. 15 - Prob. 19TCh. 15 - Prob. 20TCh. 15 - Prob. 21TCh. 15 - Prob. 22TCh. 15 - Prob. 23TCh. 15 - Prob. 24TCh. 15 - Prob. 25TCh. 15 - Prob. 1CRCh. 15 - Prob. 2CRCh. 15 - Prob. 3CRCh. 15 - Prob. 4CRCh. 15 - Prob. 5CRCh. 15 - Prob. 6CRCh. 15 - Prob. 7CRCh. 15 - Prob. 8CRCh. 15 - Prob. 9CRCh. 15 - Prob. 10CRCh. 15 - Prob. 11CRCh. 15 - Prob. 12CRCh. 15 - Prob. 13CRCh. 15 - Prob. 14CRCh. 15 - Prob. 15CRCh. 15 - Prob. 16CRCh. 15 - Prob. 17CRCh. 15 - Prob. 18CRCh. 15 - Prob. 19CRCh. 15 - Prob. 20CRCh. 15 - Prob. 21CRCh. 15 - Prob. 22CRCh. 15 - Prob. 23CRCh. 15 - Prob. 24CRCh. 15 - Prob. 25CRCh. 15 - Prob. 26CRCh. 15 - Prob. 27CRCh. 15 - Prob. 28CRCh. 15 - Prob. 29CRCh. 15 - Prob. 30CRCh. 15 - Prob. 31CRCh. 15 - Prob. 32CRCh. 15 - Prob. 33CRCh. 15 - Prob. 34CRCh. 15 - Prob. 35CRCh. 15 - Prob. 36CRCh. 15 - Prob. 37CRCh. 15 - Prob. 38CRCh. 15 - Prob. 39CRCh. 15 - Prob. 40CRCh. 15 - Prob. 41CRCh. 15 - Prob. 42CR
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