ELEMENTARY&INTERMEDIATEALGEBRA>CUSTOM<
14th Edition
ISBN: 9781269152648
Author: BITTINGER
Publisher: PEARSON C
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Chapter R.2, Problem 66ES
To determine
To calculate: The number of minutes of long- distance telephone calls that Brandon made that month if he pays $7.05 this month. While Bardon pays
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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 R Solutions
ELEMENTARY&INTERMEDIATEALGEBRA>CUSTOM<
Ch. R.1 - Prob. 1YTCh. R.1 - Prob. 2YTCh. R.1 - Prob. 3YTCh. R.1 - Prob. 4YTCh. R.1 - Prob. 5YTCh. R.1 - Prob. 6YTCh. R.1 - Prob. 7YTCh. R.1 - Prob. 8YTCh. R.1 - Prob. 9YTCh. R.1 - Prob. 1ES
Ch. R.1 - Prob. 2ESCh. R.1 - Prob. 3ESCh. R.1 - Prob. 4ESCh. R.1 - Prob. 5ESCh. R.1 - Prob. 6ESCh. R.1 - Prob. 7ESCh. R.1 - Prob. 8ESCh. R.1 - Prob. 9ESCh. R.1 - Prob. 10ESCh. R.1 - Prob. 11ESCh. R.1 - Prob. 12ESCh. R.1 - Prob. 13ESCh. R.1 - Prob. 14ESCh. R.1 - Prob. 15ESCh. R.1 - Prob. 16ESCh. R.1 - Prob. 17ESCh. R.1 - Prob. 18ESCh. R.1 - Prob. 19ESCh. R.1 - Prob. 20ESCh. R.1 - Prob. 21ESCh. R.1 - Prob. 22ESCh. R.1 - Prob. 23ESCh. R.1 - Prob. 24ESCh. R.1 - Prob. 25ESCh. R.1 - Prob. 26ESCh. R.1 - Prob. 27ESCh. R.1 - Prob. 28ESCh. R.1 - Prob. 29ESCh. R.1 - Prob. 30ESCh. R.1 - Prob. 31ESCh. R.1 - Prob. 32ESCh. R.1 - Prob. 33ESCh. R.1 - Prob. 34ESCh. R.1 - Prob. 35ESCh. R.1 - Prob. 36ESCh. R.1 - Prob. 37ESCh. R.1 - Prob. 38ESCh. R.1 - Prob. 39ESCh. R.1 - Prob. 40ESCh. R.1 - Prob. 41ESCh. R.1 - Prob. 42ESCh. R.1 - Prob. 43ESCh. R.1 - Prob. 44ESCh. R.1 - Prob. 45ESCh. R.1 - Prob. 46ESCh. R.1 - Prob. 47ESCh. R.1 - Prob. 48ESCh. R.1 - Prob. 49ESCh. R.1 - Prob. 50ESCh. R.1 - Prob. 51ESCh. R.1 - Prob. 52ESCh. R.1 - Prob. 53ESCh. R.1 - Prob. 54ESCh. R.1 - Prob. 55ESCh. R.1 - Prob. 56ESCh. R.1 - Prob. 57ESCh. R.1 - Prob. 58ESCh. R.1 - Prob. 59ESCh. R.1 - Prob. 60ESCh. R.1 - Prob. 61ESCh. R.1 - Prob. 62ESCh. R.1 - Prob. 63ESCh. R.1 - Prob. 64ESCh. R.1 - Prob. 65ESCh. R.1 - Prob. 66ESCh. R.1 - Prob. 67ESCh. R.1 - Prob. 68ESCh. R.1 - Prob. 69ESCh. R.1 - Prob. 70ESCh. R.1 - Prob. 71ESCh. R.1 - Prob. 72ESCh. R.1 - Prob. 73ESCh. R.1 - Prob. 74ESCh. R.1 - Prob. 75ESCh. R.1 - Prob. 76ESCh. R.1 - Prob. 77ESCh. R.1 - Prob. 78ESCh. R.1 - Prob. 79ESCh. R.1 - Prob. 80ESCh. R.1 - Prob. 81ESCh. R.1 - Prob. 82ESCh. R.1 - Prob. 83ESCh. R.1 - Prob. 84ESCh. R.1 - Prob. 85ESCh. R.1 - Prob. 86ESCh. R.1 - Prob. 87ESCh. R.1 - Prob. 88ESCh. R.1 - Prob. 89ESCh. R.1 - Translate each problem to an equation. Do not...Ch. R.1 - Prob. 91ESCh. R.1 - Prob. 92ESCh. R.1 - Prob. 93ESCh. R.2 - Prob. 1YTCh. R.2 - Prob. 2YTCh. R.2 - Prob. 3YTCh. R.2 - Prob. 4YTCh. R.2 - Prob. 5YTCh. R.2 - Prob. 6YTCh. R.2 - Prob. 7YTCh. R.2 - Prob. 8YTCh. R.2 - Prob. 1ESCh. R.2 - Prob. 2ESCh. R.2 - Prob. 3ESCh. R.2 - Prob. 4ESCh. R.2 - Prob. 5ESCh. R.2 - Prob. 6ESCh. R.2 - Prob. 7ESCh. R.2 - Prob. 8ESCh. R.2 - Prob. 9ESCh. R.2 - Prob. 10ESCh. R.2 - Prob. 11ESCh. R.2 - Prob. 12ESCh. R.2 - Prob. 13ESCh. R.2 - Prob. 14ESCh. R.2 - Prob. 15ESCh. R.2 - Prob. 16ESCh. R.2 - Prob. 17ESCh. R.2 - Prob. 18ESCh. R.2 - Prob. 19ESCh. R.2 - Prob. 20ESCh. R.2 - Prob. 21ESCh. R.2 - Prob. 22ESCh. R.2 - Prob. 23ESCh. R.2 - Prob. 24ESCh. R.2 - Prob. 25ESCh. R.2 - Prob. 26ESCh. R.2 - Prob. 27ESCh. R.2 - Prob. 28ESCh. R.2 - Prob. 29ESCh. R.2 - Prob. 30ESCh. R.2 - Prob. 31ESCh. R.2 - Prob. 32ESCh. R.2 - Prob. 33ESCh. R.2 - Prob. 34ESCh. R.2 - Prob. 35ESCh. R.2 - Prob. 36ESCh. R.2 - Prob. 37ESCh. R.2 - Prob. 38ESCh. R.2 - Prob. 39ESCh. R.2 - Prob. 40ESCh. R.2 - Prob. 41ESCh. R.2 - Prob. 42ESCh. R.2 - Prob. 43ESCh. R.2 - Prob. 44ESCh. R.2 - Prob. 45ESCh. R.2 - Prob. 46ESCh. R.2 - Prob. 47ESCh. R.2 - Prob. 48ESCh. R.2 - Prob. 49ESCh. R.2 - Prob. 50ESCh. R.2 - Prob. 51ESCh. R.2 - Prob. 52ESCh. R.2 - Prob. 53ESCh. R.2 - Prob. 54ESCh. R.2 - Prob. 55ESCh. R.2 - Prob. 56ESCh. R.2 - Prob. 57ESCh. R.2 - Prob. 58ESCh. R.2 - Prob. 59ESCh. R.2 - Prob. 60ESCh. R.2 - Prob. 61ESCh. R.2 - Prob. 62ESCh. R.2 - Prob. 63ESCh. R.2 - Prob. 64ESCh. R.2 - Prob. 65ESCh. R.2 - Prob. 66ESCh. R.2 - Prob. 67ESCh. R.2 - Prob. 68ESCh. R.2 - Prob. 69ESCh. R.2 - Prob. 70ESCh. R.2 - Prob. 71ESCh. R.2 - Prob. 72ESCh. R.3 - Prob. 1YTCh. R.3 - Prob. 2YTCh. R.3 - Prob. 3YTCh. R.3 - Prob. 4YTCh. R.3 - Prob. 5YTCh. R.3 - Prob. 6YTCh. R.3 - Prob. 7YTCh. R.3 - Prob. 8YTCh. R.3 - Prob. 1ESCh. R.3 - Prob. 2ESCh. R.3 - Prob. 3ESCh. R.3 - Prob. 4ESCh. R.3 - Prob. 5ESCh. R.3 - Prob. 6ESCh. R.3 - Prob. 7ESCh. R.3 - Prob. 8ESCh. R.3 - Prob. 9ESCh. R.3 - Prob. 10ESCh. R.3 - Prob. 11ESCh. R.3 - Prob. 12ESCh. R.3 - Prob. 13ESCh. R.3 - Prob. 14ESCh. R.3 - Prob. 15ESCh. R.3 - Prob. 16ESCh. R.3 - Prob. 17ESCh. R.3 - Prob. 18ESCh. R.3 - Prob. 19ESCh. R.3 - Prob. 20ESCh. R.3 - Prob. 21ESCh. R.3 - Prob. 22ESCh. R.3 - Prob. 23ESCh. R.3 - Prob. 24ESCh. R.3 - Prob. 25ESCh. R.3 - Prob. 26ESCh. R.3 - Prob. 27ESCh. R.3 - Prob. 28ESCh. R.3 - Prob. 29ESCh. R.3 - Prob. 30ESCh. R.3 - Prob. 31ESCh. R.3 - Prob. 32ESCh. R.3 - Prob. 33ESCh. R.3 - Prob. 34ESCh. R.3 - Prob. 35ESCh. R.3 - Prob. 36ESCh. R.3 - Prob. 37ESCh. R.3 - Prob. 38ESCh. R.3 - Prob. 39ESCh. R.3 - Prob. 40ESCh. R.3 - Prob. 41ESCh. R.3 - Prob. 42ESCh. R.3 - Prob. 43ESCh. R.3 - Prob. 44ESCh. R.3 - Prob. 45ESCh. R.3 - Prob. 46ESCh. R.4 - Prob. 1YTCh. R.4 - Prob. 2YTCh. R.4 - 3. Combine like terms:
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Write the answer in...Ch. R.4 - Prob. 4YTCh. R.4 - Prob. 5YTCh. R.4 - Prob. 6YTCh. R.4 - Prob. 7YTCh. R.4 - Prob. 8YTCh. R.4 - Prob. 9YTCh. R.4 - Prob. 10YTCh. R.4 - Prob. 11YTCh. R.4 - Prob. 12YTCh. R.4 - Prob. 1ESCh. R.4 - Prob. 2ESCh. R.4 - Prob. 3ESCh. R.4 - Prob. 4ESCh. R.4 - Prob. 5ESCh. R.4 - Prob. 6ESCh. R.4 - Prob. 7ESCh. R.4 - Prob. 8ESCh. R.4 - Prob. 9ESCh. R.4 - Prob. 10ESCh. R.4 - Prob. 11ESCh. R.4 - Prob. 12ESCh. R.4 - Prob. 13ESCh. R.4 - Prob. 14ESCh. R.4 - Prob. 15ESCh. R.4 - Prob. 16ESCh. R.4 - Prob. 17ESCh. R.4 - Prob. 18ESCh. R.4 - Prob. 19ESCh. R.4 - Prob. 20ESCh. R.4 - Prob. 21ESCh. R.4 - Prob. 22ESCh. R.4 - Prob. 23ESCh. R.4 - Prob. 24ESCh. R.4 - Prob. 25ESCh. R.4 - Prob. 26ESCh. R.4 - Identify the terms of each polynomial.
27.
Ch. R.4 - Identify the terms of each polynomial.
28.
Ch. R.4 - Determine the coefficient and the degree of each...Ch. R.4 - Prob. 30ESCh. R.4 - Determine the coefficient and the degree of each...Ch. R.4 - Determine the coefficient and the degree of each...Ch. R.4 - Prob. 33ESCh. R.4 - Prob. 34ESCh. R.4 - Prob. 35ESCh. R.4 - Prob. 36ESCh. R.4 - Prob. 37ESCh. R.4 - Prob. 38ESCh. R.4 - Prob. 39ESCh. R.4 - Prob. 40ESCh. R.4 - Prob. 41ESCh. R.4 - Prob. 42ESCh. R.4 - Prob. 43ESCh. R.4 - Prob. 44ESCh. R.4 - Prob. 45ESCh. R.4 - Prob. 46ESCh. R.4 - Prob. 47ESCh. R.4 - Prob. 48ESCh. R.4 - Prob. 49ESCh. R.4 - Prob. 50ESCh. R.4 - Prob. 51ESCh. R.4 - Prob. 52ESCh. R.4 - Prob. 53ESCh. R.4 - Prob. 54ESCh. R.4 - Prob. 55ESCh. R.4 - Prob. 56ESCh. R.4 - Prob. 57ESCh. R.4 - Prob. 58ESCh. R.4 - Prob. 59ESCh. R.4 - Prob. 60ESCh. R.4 - Prob. 61ESCh. R.4 - Prob. 62ESCh. R.4 - Prob. 63ESCh. R.4 - Prob. 64ESCh. R.4 - Prob. 65ESCh. R.4 - Prob. 66ESCh. R.4 - Prob. 67ESCh. R.4 - Prob. 68ESCh. R.4 - Prob. 69ESCh. R.4 - Prob. 70ESCh. R.4 - Prob. 71ESCh. R.4 - Prob. 72ESCh. R.5 - Prob. 1YTCh. R.5 - Prob. 2YTCh. R.5 - Prob. 3YTCh. R.5 - Prob. 4YTCh. R.5 - Prob. 5YTCh. R.5 - Prob. 6YTCh. R.5 - Prob. 7YTCh. R.5 - Prob. 8YTCh. R.5 - Prob. 9YTCh. R.5 - Prob. 1ESCh. R.5 - Prob. 2ESCh. R.5 - Prob. 3ESCh. R.5 - Prob. 4ESCh. R.5 - Prob. 5ESCh. R.5 - Prob. 6ESCh. R.5 - Prob. 7ESCh. R.5 - Prob. 8ESCh. R.5 - Prob. 9ESCh. R.5 - Prob. 10ESCh. R.5 - Prob. 11ESCh. R.5 - Prob. 12ESCh. R.5 - Prob. 13ESCh. R.5 - Prob. 14ESCh. R.5 - Prob. 15ESCh. R.5 - Prob. 16ESCh. R.5 - Prob. 17ESCh. R.5 - Prob. 18ESCh. R.5 - Prob. 19ESCh. R.5 - Prob. 20ESCh. R.5 - Prob. 21ESCh. R.5 - Prob. 22ESCh. R.5 - Prob. 23ESCh. R.5 - Prob. 24ESCh. R.5 - Prob. 25ESCh. R.5 - Prob. 26ESCh. R.5 - Prob. 27ESCh. R.5 - Prob. 28ESCh. R.5 - Prob. 29ESCh. R.5 - Prob. 30ESCh. R.5 - Prob. 31ESCh. R.5 - Prob. 32ESCh. R.5 - Prob. 33ESCh. R.5 - Prob. 34ESCh. R.5 - Prob. 35ESCh. R.5 - Prob. 36ESCh. R.5 - Prob. 37ESCh. R.5 - Prob. 38ESCh. R.5 - Prob. 39ESCh. R.5 - Prob. 40ESCh. R.5 - Prob. 41ESCh. R.5 - Prob. 42ESCh. R.5 - Prob. 43ESCh. R.5 - Prob. 44ESCh. R.5 - Prob. 45ESCh. R.5 - Prob. 46ESCh. R.5 - Prob. 47ESCh. R.5 - 48. Page Numbers. The product of the page numbers...Ch. R.5 - Prob. 49ESCh. R.5 - Prob. 50ESCh. R.6 - Prob. 1YTCh. R.6 - Prob. 2YTCh. R.6 - Prob. 3YTCh. R.6 - Prob. 4YTCh. R.6 - Prob. 5YTCh. R.6 - Prob. 6YTCh. R.6 - Prob. 7YTCh. R.6 - Prob. 8YTCh. R.6 - Prob. 9YTCh. R.6 - Prob. 10YTCh. R.6 - Prob. 11YTCh. R.6 - Prob. 12YTCh. R.6 - Prob. 1ESCh. R.6 - Prob. 2ESCh. R.6 - Prob. 3ESCh. R.6 - Prob. 4ESCh. R.6 - Prob. 5ESCh. R.6 - Prob. 6ESCh. R.6 - Prob. 7ESCh. R.6 - Prob. 8ESCh. R.6 - Prob. 9ESCh. R.6 - Prob. 10ESCh. R.6 - Prob. 11ESCh. R.6 - Prob. 12ESCh. R.6 - Prob. 13ESCh. R.6 - Prob. 14ESCh. R.6 - Prob. 15ESCh. R.6 - Prob. 16ESCh. R.6 - Prob. 17ESCh. R.6 - Prob. 18ESCh. R.6 - Prob. 19ESCh. R.6 - Prob. 20ESCh. R.6 - Prob. 21ESCh. R.6 - Prob. 22ESCh. R.6 - Prob. 23ESCh. R.6 - Prob. 24ESCh. R.6 - Prob. 25ESCh. R.6 - Prob. 26ESCh. R.6 - Prob. 27ESCh. R.6 - Prob. 28ESCh. R.6 - Prob. 29ESCh. R.6 - Prob. 30ESCh. R.6 - Prob. 31ESCh. R.6 - Prob. 32ESCh. R.6 - Prob. 33ESCh. R.6 - Prob. 34ESCh. R.6 - Prob. 35ESCh. R.6 - Prob. 36ESCh. R.6 - Prob. 37ESCh. R.6 - Prob. 38ESCh. R.6 - Prob. 39ESCh. R.6 - Prob. 40ESCh. R.6 - Prob. 41ESCh. R.6 - Prob. 42ESCh. R.6 - Prob. 43ESCh. R.6 - Prob. 44ESCh. R.6 - Prob. 45ESCh. R.6 - Prob. 46ESCh. R.6 - Prob. 47ESCh. R.6 - Prob. 48ESCh. R.6 - Prob. 49ESCh. R.6 - Prob. 50ESCh. R.6 - Prob. 51ESCh. R.6 - Prob. 52ESCh. R.6 - Prob. 53ESCh. R.6 - Prob. 54ESCh. R.6 - Prob. 55ESCh. R.6 - Prob. 56ES
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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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