Algebra And Trigonometry (11th Edition)
11th Edition
ISBN: 9780135163078
Author: Michael Sullivan
Publisher: PEARSON
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Question
Chapter 8.4, Problem 22AYU
To determine
To establish: The identity
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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 8 Solutions
Algebra And Trigonometry (11th Edition)
Ch. 8.1 - Prob. 1AYUCh. 8.1 - Prob. 2AYUCh. 8.1 - Prob. 3AYUCh. 8.1 - Prob. 4AYUCh. 8.1 - Prob. 5AYUCh. 8.1 - Prob. 6AYUCh. 8.1 - Prob. 7AYUCh. 8.1 - Prob. 8AYUCh. 8.1 - Prob. 9AYUCh. 8.1 - Prob. 10AYU
Ch. 8.1 - Prob. 11AYUCh. 8.1 - Prob. 12AYUCh. 8.1 - Prob. 13AYUCh. 8.1 - Prob. 14AYUCh. 8.1 - Prob. 15AYUCh. 8.1 - Prob. 16AYUCh. 8.1 - Prob. 17AYUCh. 8.1 - Prob. 18AYUCh. 8.1 - Prob. 19AYUCh. 8.1 - Prob. 20AYUCh. 8.1 - Prob. 21AYUCh. 8.1 - Prob. 22AYUCh. 8.1 - Prob. 23AYUCh. 8.1 - Prob. 24AYUCh. 8.1 - Prob. 25AYUCh. 8.1 - Prob. 26AYUCh. 8.1 - Prob. 27AYUCh. 8.1 - Prob. 28AYUCh. 8.1 - Prob. 29AYUCh. 8.1 - Prob. 30AYUCh. 8.1 - Prob. 31AYUCh. 8.1 - Prob. 32AYUCh. 8.1 - Prob. 33AYUCh. 8.1 - Prob. 34AYUCh. 8.1 - Prob. 35AYUCh. 8.1 - Prob. 36AYUCh. 8.1 - Prob. 37AYUCh. 8.1 - Prob. 38AYUCh. 8.1 - Prob. 39AYUCh. 8.1 - Prob. 40AYUCh. 8.1 - Prob. 41AYUCh. 8.1 - Prob. 42AYUCh. 8.1 - Prob. 43AYUCh. 8.1 - Prob. 44AYUCh. 8.1 - Prob. 45AYUCh. 8.1 - Prob. 46AYUCh. 8.1 - Prob. 47AYUCh. 8.1 - Prob. 48AYUCh. 8.1 - Prob. 49AYUCh. 8.1 - Prob. 50AYUCh. 8.1 - Prob. 51AYUCh. 8.1 - Prob. 52AYUCh. 8.1 - Prob. 53AYUCh. 8.1 - Prob. 54AYUCh. 8.1 - Prob. 55AYUCh. 8.1 - Prob. 56AYUCh. 8.1 - Prob. 57AYUCh. 8.1 - Prob. 58AYUCh. 8.1 - 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Prob. 15AYUCh. 8.4 - Prob. 16AYUCh. 8.4 - Prob. 17AYUCh. 8.4 - Prob. 18AYUCh. 8.4 - Prob. 19AYUCh. 8.4 - Prob. 20AYUCh. 8.4 - Prob. 21AYUCh. 8.4 - Prob. 22AYUCh. 8.4 - Prob. 23AYUCh. 8.4 - Prob. 24AYUCh. 8.4 - Prob. 25AYUCh. 8.4 - Prob. 26AYUCh. 8.4 - Prob. 27AYUCh. 8.4 - Prob. 28AYUCh. 8.4 - Prob. 29AYUCh. 8.4 - Prob. 30AYUCh. 8.4 - Prob. 31AYUCh. 8.4 - Prob. 32AYUCh. 8.4 - Prob. 33AYUCh. 8.4 - Prob. 34AYUCh. 8.4 - Prob. 35AYUCh. 8.4 - Prob. 36AYUCh. 8.4 - Prob. 37AYUCh. 8.4 - Prob. 38AYUCh. 8.4 - Prob. 39AYUCh. 8.4 - Prob. 40AYUCh. 8.4 - Prob. 41AYUCh. 8.4 - Prob. 42AYUCh. 8.4 - Prob. 43AYUCh. 8.4 - Prob. 44AYUCh. 8.4 - Prob. 45AYUCh. 8.4 - Prob. 46AYUCh. 8.4 - Prob. 47AYUCh. 8.4 - Prob. 48AYUCh. 8.4 - Prob. 49AYUCh. 8.4 - Prob. 50AYUCh. 8.4 - Prob. 51AYUCh. 8.4 - Prob. 52AYUCh. 8.4 - Prob. 53AYUCh. 8.4 - Prob. 54AYUCh. 8.4 - Prob. 55AYUCh. 8.4 - Prob. 56AYUCh. 8.4 - Prob. 57AYUCh. 8.4 - Prob. 58AYUCh. 8.4 - Prob. 59AYUCh. 8.4 - Prob. 60AYUCh. 8.4 - Prob. 61AYUCh. 8.4 - Prob. 62AYUCh. 8.4 - 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Prob. 83AYUCh. 8.5 - Prob. 84AYUCh. 8.5 - Prob. 85AYUCh. 8.5 - Prob. 86AYUCh. 8.5 - Prob. 87AYUCh. 8.5 - Prob. 88AYUCh. 8.5 - Prob. 89AYUCh. 8.5 - Prob. 90AYUCh. 8.5 - Prob. 91AYUCh. 8.5 - Prob. 92AYUCh. 8.5 - Prob. 93AYUCh. 8.5 - Prob. 94AYUCh. 8.5 - Prob. 95AYUCh. 8.5 - Prob. 96AYUCh. 8.5 - Prob. 97AYUCh. 8.5 - Prob. 98AYUCh. 8.5 - Prob. 99AYUCh. 8.5 - Prob. 100AYUCh. 8.5 - Prob. 101AYUCh. 8.5 - Prob. 102AYUCh. 8.5 - Prob. 103AYUCh. 8.5 - Prob. 104AYUCh. 8.5 - Prob. 105AYUCh. 8.5 - Prob. 106AYUCh. 8.5 - Prob. 107AYUCh. 8.5 - Prob. 108AYUCh. 8.5 - Prob. 109AYUCh. 8.5 - Prob. 110AYUCh. 8.5 - Prob. 111AYUCh. 8.5 - Prob. 112AYUCh. 8.5 - Prob. 113AYUCh. 8.5 - Prob. 114AYUCh. 8.5 - Prob. 115AYUCh. 8.5 - Prob. 116AYUCh. 8.5 - Prob. 117AYUCh. 8.5 - Prob. 118AYUCh. 8.5 - Prob. 119AYUCh. 8.5 - Prob. 120AYUCh. 8.5 - Prob. 121AYUCh. 8.5 - Prob. 122AYUCh. 8.5 - Prob. 123AYUCh. 8.5 - Prob. 124AYUCh. 8.5 - Prob. 125AYUCh. 8.6 - Prob. 1AYUCh. 8.6 - Prob. 2AYUCh. 8.6 - Prob. 3AYUCh. 8.6 - Prob. 4AYUCh. 8.6 - Prob. 5AYUCh. 8.6 - Prob. 6AYUCh. 8.6 - Prob. 7AYUCh. 8.6 - Prob. 8AYUCh. 8.6 - Prob. 9AYUCh. 8.6 - Prob. 10AYUCh. 8.6 - Prob. 11AYUCh. 8.6 - Prob. 12AYUCh. 8.6 - Prob. 13AYUCh. 8.6 - Prob. 14AYUCh. 8.6 - Prob. 15AYUCh. 8.6 - Prob. 16AYUCh. 8.6 - Prob. 17AYUCh. 8.6 - Prob. 18AYUCh. 8.6 - Prob. 19AYUCh. 8.6 - Prob. 20AYUCh. 8.6 - Prob. 21AYUCh. 8.6 - Prob. 22AYUCh. 8.6 - Prob. 23AYUCh. 8.6 - Prob. 24AYUCh. 8.6 - Prob. 25AYUCh. 8.6 - Prob. 26AYUCh. 8.6 - Prob. 27AYUCh. 8.6 - Prob. 28AYUCh. 8.6 - Prob. 29AYUCh. 8.6 - Prob. 30AYUCh. 8.6 - Prob. 31AYUCh. 8.6 - Prob. 32AYUCh. 8.6 - Prob. 33AYUCh. 8.6 - Prob. 34AYUCh. 8.6 - Prob. 35AYUCh. 8.6 - Prob. 36AYUCh. 8.6 - Prob. 37AYUCh. 8.6 - Prob. 38AYUCh. 8.6 - Prob. 39AYUCh. 8.6 - Prob. 40AYUCh. 8.6 - Prob. 41AYUCh. 8.6 - Prob. 42AYUCh. 8.6 - Prob. 43AYUCh. 8.6 - Prob. 44AYUCh. 8.6 - Prob. 45AYUCh. 8.6 - Prob. 46AYUCh. 8.6 - Prob. 47AYUCh. 8.6 - Prob. 48AYUCh. 8.6 - Prob. 49AYUCh. 8.6 - Prob. 50AYUCh. 8.6 - Prob. 51AYUCh. 8.6 - Prob. 52AYUCh. 8.6 - Prob. 53AYUCh. 8.6 - Prob. 54AYUCh. 8.6 - Prob. 55AYUCh. 8.6 - Prob. 56AYUCh. 8.6 - Prob. 57AYUCh. 8.6 - Prob. 58AYUCh. 8.6 - Prob. 59AYUCh. 8.6 - Prob. 60AYUCh. 8.6 - Prob. 61AYUCh. 8.6 - Prob. 62AYUCh. 8.6 - Prob. 63AYUCh. 8.6 - Prob. 64AYUCh. 8.6 - Prob. 65AYUCh. 8.6 - Prob. 66AYUCh. 8.6 - Prob. 67AYUCh. 8.6 - Prob. 68AYUCh. 8.6 - Prob. 69AYUCh. 8.6 - Prob. 70AYUCh. 8.6 - Prob. 71AYUCh. 8.6 - Prob. 72AYUCh. 8.6 - Prob. 73AYUCh. 8.6 - Prob. 74AYUCh. 8.6 - Prob. 75AYUCh. 8.6 - Prob. 76AYUCh. 8.6 - Prob. 77AYUCh. 8.6 - Prob. 78AYUCh. 8.6 - Prob. 79AYUCh. 8.6 - Prob. 80AYUCh. 8.6 - Prob. 81AYUCh. 8.6 - Prob. 82AYUCh. 8.6 - Prob. 83AYUCh. 8.6 - Prob. 84AYUCh. 8.6 - Prob. 85AYUCh. 8.6 - Prob. 86AYUCh. 8.6 - Prob. 87AYUCh. 8.6 - Prob. 88AYUCh. 8.6 - Prob. 89AYUCh. 8.6 - Prob. 90AYUCh. 8.6 - Prob. 91AYUCh. 8.6 - Prob. 92AYUCh. 8.6 - Prob. 93AYUCh. 8.6 - Prob. 94AYUCh. 8.6 - Prob. 95AYUCh. 8.6 - Prob. 96AYUCh. 8.6 - Prob. 97AYUCh. 8.6 - Prob. 98AYUCh. 8.6 - Prob. 99AYUCh. 8.6 - Prob. 100AYUCh. 8.6 - Prob. 101AYUCh. 8.6 - Prob. 102AYUCh. 8.6 - Prob. 103AYUCh. 8.6 - Prob. 104AYUCh. 8.6 - Prob. 105AYUCh. 8.6 - Prob. 106AYUCh. 8.6 - Prob. 107AYUCh. 8.6 - Prob. 108AYUCh. 8.6 - Prob. 109AYUCh. 8.6 - Prob. 110AYUCh. 8.6 - Prob. 111AYUCh. 8.6 - Prob. 112AYUCh. 8.6 - Prob. 113AYUCh. 8.6 - Prob. 114AYUCh. 8.6 - Prob. 115AYUCh. 8.6 - Prob. 116AYUCh. 8.6 - Prob. 117AYUCh. 8.6 - Prob. 118AYUCh. 8.6 - Prob. 119AYUCh. 8.6 - Prob. 120AYUCh. 8.6 - Prob. 121AYUCh. 8.6 - Prob. 122AYUCh. 8.6 - Prob. 123AYUCh. 8.6 - Prob. 124AYUCh. 8.6 - Prob. 125AYUCh. 8.6 - Prob. 126AYUCh. 8.6 - Prob. 127AYUCh. 8.6 - Prob. 128AYUCh. 8.6 - Prob. 129AYUCh. 8.6 - Prob. 130AYUCh. 8.6 - Prob. 131AYUCh. 8.6 - Prob. 132AYUCh. 8.7 - Prob. 1AYUCh. 8.7 - Prob. 2AYUCh. 8.7 - Prob. 3AYUCh. 8.7 - Prob. 4AYUCh. 8.7 - Prob. 5AYUCh. 8.7 - Prob. 6AYUCh. 8.7 - Prob. 7AYUCh. 8.7 - Prob. 8AYUCh. 8.7 - Prob. 9AYUCh. 8.7 - Prob. 10AYUCh. 8.7 - Prob. 11AYUCh. 8.7 - Prob. 12AYUCh. 8.7 - Prob. 13AYUCh. 8.7 - Prob. 14AYUCh. 8.7 - Prob. 15AYUCh. 8.7 - Prob. 16AYUCh. 8.7 - Prob. 17AYUCh. 8.7 - Prob. 18AYUCh. 8.7 - Prob. 19AYUCh. 8.7 - Prob. 20AYUCh. 8.7 - Prob. 21AYUCh. 8.7 - Prob. 22AYUCh. 8.7 - Prob. 23AYUCh. 8.7 - Prob. 24AYUCh. 8.7 - Prob. 25AYUCh. 8.7 - Prob. 26AYUCh. 8.7 - Prob. 27AYUCh. 8.7 - Prob. 28AYUCh. 8.7 - Prob. 29AYUCh. 8.7 - Prob. 30AYUCh. 8.7 - Prob. 31AYUCh. 8.7 - Prob. 32AYUCh. 8.7 - Prob. 33AYUCh. 8.7 - Prob. 34AYUCh. 8.7 - Prob. 35AYUCh. 8.7 - Prob. 36AYUCh. 8.7 - Prob. 37AYUCh. 8.7 - Prob. 38AYUCh. 8.7 - Prob. 39AYUCh. 8.7 - Prob. 40AYUCh. 8.7 - Prob. 41AYUCh. 8.7 - Prob. 42AYUCh. 8.7 - Prob. 43AYUCh. 8.7 - Prob. 44AYUCh. 8.7 - Prob. 45AYUCh. 8.7 - Prob. 46AYUCh. 8.7 - Prob. 47AYUCh. 8.7 - Prob. 48AYUCh. 8.7 - Prob. 49AYUCh. 8.7 - Prob. 50AYUCh. 8.7 - Prob. 51AYUCh. 8.7 - Prob. 52AYUCh. 8.7 - Prob. 53AYUCh. 8.7 - Prob. 55AYUCh. 8.7 - Prob. 56AYUCh. 8.7 - Prob. 57AYUCh. 8.7 - Prob. 58AYUCh. 8.7 - Prob. 59AYUCh. 8.7 - Prob. 60AYUCh. 8.7 - Prob. 61AYUCh. 8.7 - Prob. 62AYUCh. 8.7 - Prob. 63AYUCh. 8.7 - Prob. 64AYUCh. 8.7 - Prob. 65AYUCh. 8.7 - Prob. 66AYUCh. 8.7 - Prob. 67AYUCh. 8.7 - Prob. 68AYUCh. 8.7 - Prob. 69AYUCh. 8.7 - Prob. 70AYUCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Prob. 63RECh. 8 - Prob. 64RECh. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Prob. 67RECh. 8 - Prob. 68RECh. 8 - Prob. 69RECh. 8 - Prob. 70RECh. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 74RECh. 8 - Prob. 75RECh. 8 - Prob. 76RECh. 8 - Prob. 77RECh. 8 - Prob. 78RECh. 8 - Prob. 79RECh. 8 - Prob. 80RECh. 8 - Prob. 81RECh. 8 - Prob. 82RECh. 8 - Prob. 83RECh. 8 - Prob. 84RECh. 8 - Prob. 85RECh. 8 - Prob. 86RECh. 8 - Prob. 87RECh. 8 - Prob. 88RECh. 8 - Prob. 89RECh. 8 - Prob. 90RECh. 8 - Prob. 91RECh. 8 - Prob. 92RECh. 8 - Prob. 93RECh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 5CTCh. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CTCh. 8 - Prob. 10CTCh. 8 - Prob. 11CTCh. 8 - Prob. 12CTCh. 8 - Prob. 13CTCh. 8 - Prob. 14CTCh. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 19CTCh. 8 - Prob. 20CTCh. 8 - Prob. 21CTCh. 8 - Prob. 22CTCh. 8 - Prob. 23CTCh. 8 - Prob. 24CTCh. 8 - Prob. 25CTCh. 8 - Prob. 26CTCh. 8 - Prob. 27CTCh. 8 - Prob. 28CTCh. 8 - Prob. 29CTCh. 8 - Prob. 30CTCh. 8 - Prob. 31CTCh. 8 - Prob. 32CTCh. 8 - Prob. 33CTCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Prob. 8CRCh. 8 - Prob. 9CRCh. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CR
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