College Algebra: Concepts Through Functions (4th Edition)
4th Edition
ISBN: 9780134686967
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Concept explainers
Question
Chapter A.8, Problem 64AYU
To determine
To solve: The equation
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Students have asked these similar questions
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]
Question 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]
part b please
Chapter A Solutions
College Algebra: Concepts Through Functions (4th Edition)
Ch. A.1 - A(n) _____ is a letter used in algebra to...Ch. A.1 - Prob. 2AYUCh. A.1 - Prob. 3AYUCh. A.1 - Prob. 4AYUCh. A.1 - Prob. 5AYUCh. A.1 - Prob. 6AYUCh. A.1 - Prob. 7AYUCh. A.1 - Prob. 8AYUCh. A.1 - Prob. 9AYUCh. A.1 - Prob. 10AYU
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A.7 - Prob. 73AYUCh. A.7 - Prob. 74AYUCh. A.7 - Prob. 75AYUCh. A.7 - Prob. 76AYUCh. A.7 - Prob. 77AYUCh. A.7 - Prob. 78AYUCh. A.7 - Prob. 79AYUCh. A.7 - Prob. 80AYUCh. A.7 - Prob. 81AYUCh. A.7 - Prob. 82AYUCh. A.7 - Prob. 83AYUCh. A.7 - Prob. 84AYUCh. A.7 - Prob. 85AYUCh. A.7 - Prob. 86AYUCh. A.7 - Prob. 87AYUCh. A.7 - Prob. 88AYUCh. A.7 - Prob. 89AYUCh. A.7 - Prob. 90AYUCh. A.7 - Prob. 91AYUCh. A.7 - Prob. 92AYUCh. A.7 - Prob. 93AYUCh. A.7 - Prob. 94AYUCh. A.7 - Prob. 95AYUCh. A.7 - Prob. 96AYUCh. A.7 - Prob. 97AYUCh. A.7 - Prob. 98AYUCh. A.7 - Prob. 99AYUCh. A.7 - Prob. 100AYUCh. A.7 - Prob. 101AYUCh. A.7 - Prob. 102AYUCh. A.7 - Prob. 103AYUCh. A.7 - Prob. 104AYUCh. A.7 - Prob. 105AYUCh. A.7 - Prob. 106AYUCh. A.7 - Prob. 107AYUCh. A.7 - Prob. 108AYUCh. A.7 - Prob. 109AYUCh. A.7 - Prob. 110AYUCh. A.7 - Prob. 111AYUCh. A.7 - Prob. 112AYUCh. A.7 - Prob. 113AYUCh. A.7 - Prob. 114AYUCh. A.7 - Prob. 115AYUCh. A.7 - Prob. 116AYUCh. A.7 - Prob. 117AYUCh. A.7 - Prob. 118AYUCh. A.7 - Prob. 119AYUCh. A.7 - Prob. 120AYUCh. A.7 - Prob. 121AYUCh. A.7 - Prob. 122AYUCh. A.7 - Prob. 123AYUCh. A.7 - Prob. 124AYUCh. A.7 - Prob. 125AYUCh. A.7 - Prob. 126AYUCh. A.7 - Prob. 127AYUCh. A.7 - Prob. 128AYUCh. A.7 - Prob. 129AYUCh. A.8 - Prob. 1AYUCh. A.8 - Prob. 2AYUCh. A.8 - Prob. 3AYUCh. A.8 - Prob. 4AYUCh. A.8 - Prob. 5AYUCh. A.8 - Prob. 6AYUCh. A.8 - Prob. 7AYUCh. A.8 - Prob. 8AYUCh. A.8 - Prob. 9AYUCh. A.8 - Prob. 10AYUCh. A.8 - Prob. 11AYUCh. A.8 - Prob. 12AYUCh. A.8 - Prob. 13AYUCh. A.8 - Prob. 14AYUCh. A.8 - Prob. 15AYUCh. A.8 - Prob. 16AYUCh. A.8 - Prob. 17AYUCh. A.8 - Prob. 18AYUCh. A.8 - Prob. 19AYUCh. A.8 - Prob. 20AYUCh. A.8 - Prob. 21AYUCh. A.8 - Prob. 22AYUCh. A.8 - Prob. 23AYUCh. A.8 - Prob. 24AYUCh. A.8 - Prob. 25AYUCh. A.8 - Prob. 26AYUCh. A.8 - Prob. 27AYUCh. A.8 - Prob. 28AYUCh. A.8 - Prob. 29AYUCh. A.8 - Prob. 30AYUCh. A.8 - Prob. 31AYUCh. A.8 - Prob. 32AYUCh. A.8 - Prob. 33AYUCh. A.8 - Prob. 34AYUCh. A.8 - Prob. 35AYUCh. A.8 - Prob. 36AYUCh. A.8 - Prob. 37AYUCh. A.8 - Prob. 38AYUCh. A.8 - Prob. 39AYUCh. A.8 - Prob. 40AYUCh. A.8 - Prob. 41AYUCh. A.8 - Prob. 42AYUCh. A.8 - Prob. 43AYUCh. A.8 - Prob. 44AYUCh. A.8 - Prob. 45AYUCh. A.8 - Prob. 46AYUCh. A.8 - Prob. 47AYUCh. A.8 - Prob. 48AYUCh. A.8 - Prob. 49AYUCh. A.8 - Prob. 50AYUCh. A.8 - Prob. 51AYUCh. A.8 - Prob. 52AYUCh. A.8 - Prob. 53AYUCh. A.8 - Prob. 54AYUCh. A.8 - Prob. 55AYUCh. A.8 - Prob. 56AYUCh. A.8 - Prob. 57AYUCh. A.8 - Prob. 58AYUCh. A.8 - Prob. 59AYUCh. A.8 - Prob. 60AYUCh. A.8 - Prob. 61AYUCh. A.8 - Prob. 62AYUCh. A.8 - Prob. 63AYUCh. A.8 - Prob. 64AYUCh. A.8 - Prob. 65AYUCh. A.8 - Prob. 66AYUCh. A.8 - Prob. 67AYUCh. A.8 - Prob. 68AYUCh. A.8 - Prob. 69AYUCh. A.8 - Prob. 70AYUCh. A.8 - Prob. 71AYUCh. A.8 - Prob. 72AYUCh. A.8 - Prob. 73AYUCh. A.8 - Prob. 74AYUCh. A.8 - Physics: Using Sound to Measure Distance The...Ch. A.8 - Prob. 76AYUCh. A.8 - Prob. 77AYUCh. A.8 - Prob. 78AYUCh. A.8 - Prob. 79AYUCh. A.8 - Prob. 80AYUCh. A.8 - Prob. 81AYUCh. A.8 - Prob. 82AYUCh. A.8 - Prob. 83AYUCh. A.8 - Prob. 84AYUCh. A.9 - Prob. 1AYUCh. A.9 - Prob. 2AYUCh. A.9 - Prob. 3AYUCh. A.9 - Prob. 4AYUCh. A.9 - True or False If an object moves at an average...Ch. A.9 - Prob. 6AYUCh. A.9 - Prob. 7AYUCh. A.9 - If it takes 5 hours to complete a job, what...Ch. A.9 - Prob. 9AYUCh. A.9 - Prob. 10AYUCh. A.9 - Prob. 11AYUCh. A.9 - Prob. 12AYUCh. A.9 - Prob. 13AYUCh. A.9 - Prob. 14AYUCh. A.9 - Prob. 15AYUCh. A.9 - Prob. 16AYUCh. A.9 - Prob. 17AYUCh. A.9 - Prob. 18AYUCh. A.9 - Prob. 19AYUCh. A.9 - Prob. 20AYUCh. A.9 - Prob. 21AYUCh. A.9 - Prob. 22AYUCh. A.9 - Prob. 23AYUCh. A.9 - Prob. 24AYUCh. A.9 - Prob. 25AYUCh. A.9 - Prob. 26AYUCh. A.9 - Prob. 27AYUCh. A.9 - Prob. 28AYUCh. A.9 - Prob. 29AYUCh. A.9 - Prob. 30AYUCh. A.9 - Prob. 31AYUCh. A.9 - Prob. 32AYUCh. A.9 - Prob. 33AYUCh. A.9 - Prob. 34AYUCh. A.9 - Prob. 35AYUCh. A.9 - Prob. 36AYUCh. A.9 - Prob. 37AYUCh. A.9 - Prob. 38AYUCh. A.9 - Prob. 39AYUCh. A.9 - Prob. 40AYUCh. A.9 - Prob. 41AYUCh. A.9 - Prob. 42AYUCh. A.9 - Prob. 43AYUCh. A.9 - Prob. 44AYUCh. A.9 - Prob. 45AYUCh. A.9 - Prob. 46AYUCh. A.9 - Prob. 47AYUCh. A.9 - Prob. 48AYUCh. A.9 - Prob. 49AYUCh. A.9 - Prob. 50AYUCh. A.9 - Prob. 51AYUCh. A.9 - Prob. 52AYUCh. A.9 - Prob. 53AYUCh. A.9 - Prob. 54AYUCh. A.9 - Prob. 55AYUCh. A.9 - Prob. 56AYUCh. A.9 - Prob. 57AYUCh. A.9 - Prob. 59AYUCh. A.9 - Prob. 60AYUCh. A.9 - Prob. 61AYUCh. A.10 - Prob. 1AYUCh. A.10 - Prob. 2AYUCh. A.10 - Prob. 3AYUCh. A.10 - Prob. 4AYUCh. A.10 - The _____ _____ states that the sense, or...Ch. A.10 - Prob. 6AYUCh. A.10 - Prob. 7AYUCh. A.10 - Prob. 8AYUCh. A.10 - Prob. 9AYUCh. A.10 - Prob. 10AYUCh. A.10 - Prob. 11AYUCh. A.10 - Prob. 12AYUCh. A.10 - Prob. 13AYUCh. A.10 - Prob. 14AYUCh. A.10 - Prob. 15AYUCh. A.10 - Prob. 16AYUCh. A.10 - Prob. 17AYUCh. A.10 - Prob. 18AYUCh. A.10 - Prob. 19AYUCh. A.10 - Prob. 20AYUCh. A.10 - Prob. 21AYUCh. A.10 - Prob. 22AYUCh. A.10 - Prob. 23AYUCh. A.10 - Prob. 24AYUCh. A.10 - Prob. 25AYUCh. A.10 - Prob. 26AYUCh. A.10 - Prob. 27AYUCh. A.10 - Prob. 28AYUCh. A.10 - Prob. 29AYUCh. A.10 - Prob. 30AYUCh. A.10 - Prob. 31AYUCh. A.10 - Prob. 32AYUCh. A.10 - Prob. 33AYUCh. A.10 - Prob. 34AYUCh. A.10 - Prob. 35AYUCh. A.10 - Prob. 36AYUCh. A.10 - Prob. 37AYUCh. A.10 - Prob. 38AYUCh. A.10 - Prob. 39AYUCh. A.10 - Prob. 40AYUCh. A.10 - Prob. 41AYUCh. A.10 - Prob. 42AYUCh. A.10 - Prob. 43AYUCh. A.10 - Prob. 44AYUCh. A.10 - Prob. 45AYUCh. A.10 - Prob. 46AYUCh. A.10 - Prob. 47AYUCh. A.10 - Prob. 48AYUCh. A.10 - Prob. 49AYUCh. A.10 - Prob. 50AYUCh. A.10 - Prob. 51AYUCh. A.10 - Prob. 52AYUCh. A.10 - Prob. 53AYUCh. A.10 - Prob. 54AYUCh. A.10 - Prob. 55AYUCh. A.10 - Prob. 56AYUCh. A.10 - Prob. 57AYUCh. A.10 - Prob. 58AYUCh. A.10 - Prob. 59AYUCh. A.10 - Prob. 60AYUCh. A.10 - Prob. 61AYUCh. A.10 - Prob. 62AYUCh. A.10 - Prob. 63AYUCh. A.10 - Prob. 64AYUCh. A.10 - Prob. 65AYUCh. A.10 - Prob. 66AYUCh. A.10 - Prob. 67AYUCh. A.10 - Prob. 68AYUCh. A.10 - Prob. 69AYUCh. A.10 - Prob. 70AYUCh. A.10 - Prob. 71AYUCh. A.10 - Prob. 72AYUCh. A.10 - Prob. 73AYUCh. A.10 - Prob. 74AYUCh. A.10 - Prob. 75AYUCh. A.10 - Prob. 76AYUCh. A.10 - Prob. 77AYUCh. A.10 - Prob. 78AYUCh. A.10 - Prob. 79AYUCh. A.10 - Prob. 80AYUCh. A.10 - Prob. 81AYUCh. A.10 - Prob. 82AYUCh. A.10 - Prob. 83AYUCh. A.10 - Prob. 84AYUCh. A.10 - Prob. 85AYUCh. A.10 - Prob. 86AYUCh. A.10 - Prob. 87AYUCh. A.10 - Prob. 88AYUCh. A.10 - Prob. 89AYUCh. A.10 - Prob. 90AYUCh. A.10 - Prob. 91AYUCh. A.10 - Prob. 92AYUCh. A.10 - Prob. 93AYUCh. A.10 - Prob. 94AYUCh. A.10 - Prob. 95AYUCh. A.10 - Prob. 96AYUCh. A.10 - Prob. 97AYUCh. A.10 - Prob. 98AYUCh. A.10 - Prob. 99AYUCh. A.10 - Prob. 100AYUCh. A.10 - Prob. 101AYUCh. A.10 - Prob. 102AYUCh. A.10 - Prob. 103AYUCh. A.10 - Prob. 104AYUCh. A.10 - Prob. 105AYUCh. A.10 - Prob. 106AYUCh. A.10 - Prob. 107AYUCh. A.10 - Prob. 108AYUCh. A.10 - Prob. 109AYUCh. A.10 - Prob. 110AYUCh. A.10 - Prob. 111AYUCh. A.10 - Prob. 112AYUCh. A.10 - Prob. 113AYUCh. A.10 - Prob. 114AYUCh. A.10 - Prob. 115AYUCh. A.10 - Prob. 116AYUCh. A.10 - Prob. 117AYUCh. A.10 - Prob. 118AYUCh. A.10 - Prob. 119AYUCh. A.10 - Prob. 120AYUCh. A.11 - Prob. 1AYUCh. A.11 - Prob. 2AYUCh. A.11 - Prob. 3AYUCh. A.11 - Prob. 4AYUCh. A.11 - Prob. 5AYUCh. A.11 - Prob. 6AYUCh. A.11 - Prob. 7AYUCh. A.11 - Prob. 8AYUCh. A.11 - Prob. 9AYUCh. A.11 - Prob. 10AYUCh. A.11 - Prob. 11AYUCh. A.11 - Prob. 12AYUCh. A.11 - Prob. 13AYUCh. A.11 - Prob. 14AYUCh. A.11 - Prob. 15AYUCh. A.11 - Prob. 16AYUCh. A.11 - Prob. 17AYUCh. A.11 - Prob. 18AYUCh. A.11 - Prob. 19AYUCh. A.11 - Prob. 20AYUCh. A.11 - Prob. 21AYUCh. A.11 - Prob. 22AYUCh. A.11 - Prob. 23AYUCh. A.11 - Prob. 24AYUCh. A.11 - Prob. 25AYUCh. A.11 - Prob. 26AYUCh. A.11 - Prob. 27AYUCh. A.11 - Prob. 28AYUCh. A.11 - Prob. 29AYUCh. A.11 - Prob. 30AYUCh. A.11 - Prob. 31AYUCh. A.11 - Prob. 32AYUCh. A.11 - Prob. 33AYUCh. A.11 - Prob. 34AYUCh. A.11 - Prob. 35AYUCh. A.11 - Prob. 36AYUCh. A.11 - Prob. 37AYUCh. A.11 - Prob. 38AYUCh. A.11 - Prob. 39AYUCh. A.11 - Prob. 40AYUCh. A.11 - Prob. 41AYUCh. A.11 - Prob. 42AYUCh. A.11 - Prob. 43AYUCh. A.11 - Prob. 44AYUCh. A.11 - Prob. 45AYUCh. A.11 - Prob. 46AYUCh. A.11 - Prob. 47AYUCh. A.11 - Prob. 48AYUCh. A.11 - Prob. 49AYUCh. A.11 - Prob. 50AYUCh. A.11 - Prob. 51AYUCh. A.11 - Prob. 52AYUCh. A.11 - Prob. 53AYUCh. A.11 - Prob. 54AYUCh. A.11 - Prob. 55AYUCh. A.11 - Prob. 56AYUCh. A.11 - Prob. 57AYUCh. A.11 - Prob. 58AYUCh. A.11 - Prob. 59AYUCh. A.11 - Prob. 60AYUCh. A.11 - Prob. 61AYUCh. A.11 - Prob. 62AYUCh. A.11 - Prob. 63AYUCh. A.11 - Prob. 64AYUCh. A.11 - Prob. 65AYUCh. A.11 - Prob. 66AYUCh. A.11 - Prob. 67AYUCh. A.11 - Prob. 68AYUCh. A.11 - Prob. 72AYUCh. A.11 - Prob. 73AYU
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