EBK CALCULUS FOR BUSINESS, ECONOMICS, L
14th Edition
ISBN: 9780134856667
Author: Stocker
Publisher: VST
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Chapter A.5, Problem 14E
To determine
To express: The expression
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16. Solve the given differential equation:
y" + 4y sin (t)u(t 2π),
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Given,
1
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1/3
-1/3
=
+
x²+1 x² +4
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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]
Chapter A.5 Solutions
EBK CALCULUS FOR BUSINESS, ECONOMICS, L
Ch. A.5 - Simplify, and express the answers using positive...Ch. A.5 - Prob. 2MPCh. A.5 - (A)Write each number in scientific notation:...Ch. A.5 - In Problems 114, simplify and express answers...Ch. A.5 - Prob. 2ECh. A.5 - Prob. 3ECh. A.5 - Prob. 4ECh. A.5 - In Problems 114, simplify and express answers...Ch. A.5 - Prob. 6ECh. A.5 - Prob. 7E
Ch. A.5 - In Problems 114, simplify and express answers...Ch. A.5 - In Problems 114, simplify and express answers...Ch. A.5 - In Problems 114, simplify and express answers...Ch. A.5 - In Problems 114, simplify and express answers...Ch. A.5 - In Problems 114, simplify and express answers...Ch. A.5 - Prob. 13ECh. A.5 - Prob. 14ECh. A.5 - Prob. 15ECh. A.5 - Prob. 16ECh. A.5 - Prob. 17ECh. A.5 - In Problems 1520, write each number in scientific...Ch. A.5 - Prob. 19ECh. A.5 - In Problems 1520, write each number in scientific...Ch. A.5 - In Problems 2128, write each number in standard...Ch. A.5 - In Problems 2128, write each number in standard...Ch. A.5 - In Problems 2128, write each number in standard...Ch. A.5 - In Problems 2128, write each number in standard...Ch. A.5 - In Problems 2128, write each number in standard...Ch. A.5 - In Problems 2128, write each number in standard...Ch. A.5 - Prob. 27ECh. A.5 - In Problems 2128, write each number in standard...Ch. A.5 - Prob. 29ECh. A.5 - Prob. 30ECh. A.5 - In Problems 2938, simplify and express answers...Ch. A.5 - In Problems 2938, simplify and express answers...Ch. A.5 - In Problems 2938, simplify and express answers...Ch. A.5 - In Problems 2938, simplify and express answers...Ch. A.5 - Prob. 35ECh. A.5 - Prob. 36ECh. A.5 - In Problems 2938, simplify and express answers...Ch. A.5 - In Problems 2938, simplify and express answers...Ch. A.5 - In Problems 3942, write each expression in the...Ch. A.5 - In Problems 3942, write each expression in the...Ch. A.5 - In Problems 3942, write each expression in the...Ch. A.5 - In Problems 3942, write each expression in the...Ch. A.5 - Write each expression in Problems 4346 with...Ch. A.5 - Write each expression in Problems 4346 with...Ch. A.5 - Write each expression in Problems 4346 with...Ch. A.5 - Prob. 46ECh. A.5 - Prob. 47ECh. A.5 - Prob. 48ECh. A.5 - Prob. 49ECh. A.5 - Prob. 50ECh. A.5 - What is the result of entering 232 on a...Ch. A.5 - Prob. 52ECh. A.5 - If n = 0, then property 1 in Theorem 1 implies...Ch. A.5 - If m = n, then property 1 in Theorem 1 implies...Ch. A.5 - Write the fractions in Problems 5558 as simple...Ch. A.5 - Prob. 56ECh. A.5 - Write the fractions in Problems 5558 as simple...Ch. A.5 - Write the fractions in Problems 5558 as simple...Ch. A.5 - Problems 59 and 60 refer to Table 1. Table 1 U.S....Ch. A.5 - Prob. 60ECh. A.5 - Prob. 61ECh. A.5 - Air pollution. Air quality standards establish...Ch. A.5 - Prob. 63ECh. A.5 - Population density. The United States had a 2016...
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