EBK ALGEBRA FOUNDATIONS
15th Edition
ISBN: 9780321978929
Author: Martin-Gay
Publisher: PEARSON
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Chapter 16.1, Problem 89ES
To determine
Tosolve: the inequality and graph the solution set and write its interval notation.
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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]
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 16 Solutions
EBK ALGEBRA FOUNDATIONS
Ch. 16.1 - Use the choices below to fill in each blank. Or ...Ch. 16.1 - Use the choices below to fill in each blank. Or ...Ch. 16.1 - Prob. 3VRVCCh. 16.1 - Prob. 4VRVCCh. 16.1 - Prob. 5VRVCCh. 16.1 - Prob. 6VRVCCh. 16.1 - Prob. 1ESCh. 16.1 - Prob. 2ESCh. 16.1 - Prob. 3ESCh. 16.1 - Prob. 4ES
Ch. 16.1 - Prob. 5ESCh. 16.1 - Prob. 6ESCh. 16.1 - Prob. 7ESCh. 16.1 - Prob. 8ESCh. 16.1 - Prob. 9ESCh. 16.1 - Prob. 10ESCh. 16.1 - Prob. 11ESCh. 16.1 - Prob. 12ESCh. 16.1 - Prob. 13ESCh. 16.1 - Prob. 14ESCh. 16.1 - Prob. 15ESCh. 16.1 - Prob. 16ESCh. 16.1 - Prob. 17ESCh. 16.1 - Prob. 18ESCh. 16.1 - Prob. 19ESCh. 16.1 - Prob. 20ESCh. 16.1 - Prob. 21ESCh. 16.1 - Prob. 22ESCh. 16.1 - Prob. 23ESCh. 16.1 - Solve each compound inequality. Write solutions in...Ch. 16.1 - Prob. 25ESCh. 16.1 - Prob. 26ESCh. 16.1 - Prob. 27ESCh. 16.1 - Prob. 28ESCh. 16.1 - Prob. 29ESCh. 16.1 - Prob. 30ESCh. 16.1 - Prob. 31ESCh. 16.1 - Prob. 32ESCh. 16.1 - Prob. 33ESCh. 16.1 - Prob. 34ESCh. 16.1 - Prob. 35ESCh. 16.1 - Prob. 36ESCh. 16.1 - Prob. 37ESCh. 16.1 - Prob. 38ESCh. 16.1 - Prob. 39ESCh. 16.1 - Prob. 40ESCh. 16.1 - Prob. 41ESCh. 16.1 - Prob. 42ESCh. 16.1 - Prob. 43ESCh. 16.1 - Prob. 44ESCh. 16.1 - Prob. 45ESCh. 16.1 - Prob. 46ESCh. 16.1 - Prob. 47ESCh. 16.1 - Objectives B D Mixed Practice Solve each compound...Ch. 16.1 - Prob. 49ESCh. 16.1 - Prob. 50ESCh. 16.1 - Prob. 51ESCh. 16.1 - Prob. 52ESCh. 16.1 - Prob. 53ESCh. 16.1 - Prob. 54ESCh. 16.1 - Prob. 55ESCh. 16.1 - Prob. 56ESCh. 16.1 - Prob. 57ESCh. 16.1 - Prob. 58ESCh. 16.1 - Prob. 59ESCh. 16.1 - Prob. 60ESCh. 16.1 - Prob. 61ESCh. 16.1 - Prob. 62ESCh. 16.1 - Prob. 63ESCh. 16.1 - Prob. 64ESCh. 16.1 - Prob. 65ESCh. 16.1 - Prob. 66ESCh. 16.1 - Prob. 67ESCh. 16.1 - Prob. 68ESCh. 16.1 - Prob. 69ESCh. 16.1 - Prob. 70ESCh. 16.1 - Prob. 71ESCh. 16.1 - Prob. 72ESCh. 16.1 - Prob. 73ESCh. 16.1 - Prob. 74ESCh. 16.1 - Prob. 75ESCh. 16.1 - Prob. 76ESCh. 16.1 - Prob. 77ESCh. 16.1 - Prob. 78ESCh. 16.1 - Prob. 79ESCh. 16.1 - Prob. 80ESCh. 16.1 - Prob. 81ESCh. 16.1 - Prob. 82ESCh. 16.1 - Prob. 83ESCh. 16.1 - Prob. 84ESCh. 16.1 - Prob. 85ESCh. 16.1 - Prob. 86ESCh. 16.1 - Prob. 87ESCh. 16.1 - Prob. 88ESCh. 16.1 - Prob. 89ESCh. 16.1 - Prob. 90ESCh. 16.1 - Prob. 91ESCh. 16.1 - Prob. 92ESCh. 16.1 - Prob. 93ESCh. 16.1 - Prob. 94ESCh. 16.2 - Match each absolute value equation with the...Ch. 16.2 - Prob. 2VRVCCh. 16.2 - Prob. 3VRVCCh. 16.2 - Prob. 4VRVCCh. 16.2 - Prob. 5VRVCCh. 16.2 - Prob. 1ESCh. 16.2 - Prob. 2ESCh. 16.2 - Prob. 3ESCh. 16.2 - Prob. 4ESCh. 16.2 - Prob. 5ESCh. 16.2 - Prob. 6ESCh. 16.2 - Prob. 7ESCh. 16.2 - Prob. 8ESCh. 16.2 - Objective A Solve each absolute value equation....Ch. 16.2 - Prob. 10ESCh. 16.2 - Prob. 11ESCh. 16.2 - Prob. 12ESCh. 16.2 - Prob. 13ESCh. 16.2 - Prob. 14ESCh. 16.2 - Prob. 15ESCh. 16.2 - Prob. 16ESCh. 16.2 - Prob. 17ESCh. 16.2 - Prob. 18ESCh. 16.2 - Prob. 19ESCh. 16.2 - Prob. 20ESCh. 16.2 - Prob. 21ESCh. 16.2 - Prob. 22ESCh. 16.2 - Prob. 23ESCh. 16.2 - Prob. 24ESCh. 16.2 - Mixed Practice Solve each absolute value equation....Ch. 16.2 - Prob. 26ESCh. 16.2 - Prob. 27ESCh. 16.2 - Prob. 28ESCh. 16.2 - Prob. 29ESCh. 16.2 - Prob. 30ESCh. 16.2 - Prob. 31ESCh. 16.2 - Prob. 32ESCh. 16.2 - Prob. 33ESCh. 16.2 - Prob. 34ESCh. 16.2 - Prob. 35ESCh. 16.2 - Prob. 36ESCh. 16.2 - Prob. 37ESCh. 16.2 - Prob. 38ESCh. 16.2 - Prob. 39ESCh. 16.2 - Prob. 40ESCh. 16.2 - Prob. 41ESCh. 16.2 - Prob. 42ESCh. 16.2 - Prob. 43ESCh. 16.2 - Prob. 44ESCh. 16.2 - Prob. 45ESCh. 16.2 - Prob. 46ESCh. 16.2 - Prob. 47ESCh. 16.2 - Prob. 48ESCh. 16.2 - Prob. 49ESCh. 16.2 - Prob. 50ESCh. 16.2 - Prob. 51ESCh. 16.2 - Prob. 52ESCh. 16.2 - Prob. 53ESCh. 16.2 - Prob. 54ESCh. 16.2 - Prob. 55ESCh. 16.2 - Prob. 56ESCh. 16.2 - Prob. 57ESCh. 16.2 - Prob. 58ESCh. 16.2 - Prob. 59ESCh. 16.2 - Prob. 60ESCh. 16.2 - Prob. 61ESCh. 16.2 - Prob. 62ESCh. 16.2 - Prob. 63ESCh. 16.2 - Prob. 64ESCh. 16.2 - Prob. 65ESCh. 16.2 - Prob. 66ESCh. 16.2 - Prob. 67ESCh. 16.2 - Prob. 68ESCh. 16.2 - Prob. 69ESCh. 16.2 - Prob. 70ESCh. 16.2 - Prob. 71ESCh. 16.2 - Prob. 72ESCh. 16.2 - Prob. 73ESCh. 16.2 - Prob. 74ESCh. 16.2 - Prob. 75ESCh. 16.2 - Prob. 76ESCh. 16.2 - Prob. 77ESCh. 16.2 - Prob. 78ESCh. 16.2 - Prob. 79ESCh. 16.2 - Prob. 80ESCh. 16.2 - Prob. 81ESCh. 16.2 - Prob. 82ESCh. 16.2 - Prob. 83ESCh. 16.2 - Prob. 84ESCh. 16.2 - Prob. 85ESCh. 16.2 - Prob. 86ESCh. 16.2 - Prob. 87ESCh. 16.2 - Prob. 88ESCh. 16.2 - Prob. 89ESCh. 16.2 - Prob. 90ESCh. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Match each absolute value statement with the...Ch. 16.3 - Prob. 1ESCh. 16.3 - Prob. 2ESCh. 16.3 - Prob. 3ESCh. 16.3 - Prob. 4ESCh. 16.3 - Prob. 5ESCh. 16.3 - Prob. 6ESCh. 16.3 - Prob. 7ESCh. 16.3 - Objective A Solve each ineqaulity. Then graph the...Ch. 16.3 - Prob. 9ESCh. 16.3 - Prob. 10ESCh. 16.3 - Prob. 11ESCh. 16.3 - Prob. 12ESCh. 16.3 - Prob. 13ESCh. 16.3 - Prob. 14ESCh. 16.3 - Prob. 15ESCh. 16.3 - Prob. 16ESCh. 16.3 - Prob. 17ESCh. 16.3 - Prob. 18ESCh. 16.3 - Prob. 19ESCh. 16.3 - Prob. 20ESCh. 16.3 - Objective B Solve each ineqaulity. Graph the...Ch. 16.3 - Prob. 22ESCh. 16.3 - Prob. 23ESCh. 16.3 - Prob. 24ESCh. 16.3 - Prob. 25ESCh. 16.3 - Prob. 26ESCh. 16.3 - Prob. 27ESCh. 16.3 - Prob. 28ESCh. 16.3 - Prob. 29ESCh. 16.3 - Prob. 30ESCh. 16.3 - Prob. 31ESCh. 16.3 - Prob. 32ESCh. 16.3 - Prob. 33ESCh. 16.3 - Prob. 34ESCh. 16.3 - Prob. 35ESCh. 16.3 - Prob. 36ESCh. 16.3 - Prob. 37ESCh. 16.3 - Prob. 38ESCh. 16.3 - Prob. 39ESCh. 16.3 - Prob. 40ESCh. 16.3 - Prob. 41ESCh. 16.3 - Prob. 42ESCh. 16.3 - Prob. 43ESCh. 16.3 - Prob. 44ESCh. 16.3 - Prob. 45ESCh. 16.3 - Prob. 46ESCh. 16.3 - Prob. 47ESCh. 16.3 - Prob. 48ESCh. 16.3 - Prob. 49ESCh. 16.3 - Prob. 50ESCh. 16.3 - Prob. 51ESCh. 16.3 - Prob. 52ESCh. 16.3 - Prob. 53ESCh. 16.3 - Prob. 54ESCh. 16.3 - Prob. 55ESCh. 16.3 - Prob. 56ESCh. 16.3 - Prob. 57ESCh. 16.3 - Prob. 58ESCh. 16.3 - Prob. 59ESCh. 16.3 - Prob. 60ESCh. 16.3 - Prob. 61ESCh. 16.3 - Prob. 62ESCh. 16.3 - Prob. 63ESCh. 16.3 - Prob. 64ESCh. 16.3 - Prob. 65ESCh. 16.3 - Prob. 66ESCh. 16.3 - Prob. 67ESCh. 16.3 - Prob. 68ESCh. 16.3 - Prob. 69ESCh. 16.3 - Prob. 70ESCh. 16.3 - Prob. 71ESCh. 16.3 - Prob. 72ESCh. 16.3 - Prob. 73ESCh. 16.3 - Prob. 74ESCh. 16.3 - Prob. 75ESCh. 16.3 - Prob. 76ESCh. 16.3 - Prob. 77ESCh. 16.3 - Prob. 78ESCh. 16.3 - Prob. 79ESCh. 16.3 - Prob. 80ESCh. 16.3 - Prob. 81ESCh. 16.3 - Prob. 82ESCh. 16.3 - Prob. 83ESCh. 16.3 - Prob. 84ESCh. 16.3 - Prob. 85ESCh. 16.3 - Prob. 86ESCh. 16.3 - Prob. 87ESCh. 16.3 - Prob. 88ESCh. 16.3 - Prob. 89ESCh. 16.3 - Prob. 90ESCh. 16.3 - Prob. 91ESCh. 16.3 - Prob. 92ESCh. 16.3 - Prob. 93ESCh. 16.3 - Prob. 94ESCh. 16.3 - Prob. 95ESCh. 16.3 - Prob. 96ESCh. 16.4 - Prob. 1VRVCCh. 16.4 - Prob. 2VRVCCh. 16.4 - Prob. 3VRVCCh. 16.4 - Prob. 4VRVCCh. 16.4 - Prob. 5VRVCCh. 16.4 - Prob. 6VRVCCh. 16.4 - Prob. 7VRVCCh. 16.4 - Prob. 8VRVCCh. 16.4 - Prob. 9VRVCCh. 16.4 - Prob. 10VRVCCh. 16.4 - Prob. 1ESCh. 16.4 - Prob. 2ESCh. 16.4 - Prob. 3ESCh. 16.4 - Prob. 4ESCh. 16.4 - Prob. 5ESCh. 16.4 - Prob. 6ESCh. 16.4 - Prob. 7ESCh. 16.4 - Prob. 8ESCh. 16.4 - Prob. 9ESCh. 16.4 - Prob. 10ESCh. 16.4 - 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