Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)
11th Edition
ISBN: 9780137554843
Author: Allyn Washington, Richard Evans
Publisher: PEARSON+
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Chapter 4, Problem 71RE
To determine
The angle between the line passing through origin and
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Let
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(a) Show that v =
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()
is an eigenvector of A and find the corresponding
(b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a)
may be useful.
(c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces.
(d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let
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A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
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eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
Chapter 4 Solutions
Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)
Ch. 4.1 - Change 17°24′ to decimal form.
Ch. 4.1 - Prob. 2PECh. 4.1 - Prob. 3PECh. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7E
Ch. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - In Exercises 15–18, by means of the definition of...Ch. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - In Exercises 19–22, use a calculator conversion...Ch. 4.1 - In Exercises 19–22, use a calculator conversion...Ch. 4.1 - In Exercises 19–22, use a calculator conversion...Ch. 4.1 - Prob. 22ECh. 4.1 - In Exercises 23–26, use a calculator conversion...Ch. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - In Exercises 31–34, change the given angles to...Ch. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - In Exercises 35–42, draw angles in standard...Ch. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - A windmill rotates 15.6 revolutions in a...Ch. 4.2 - In Example 2, change (3, 4) to (4, 3) and then...Ch. 4.2 - Prob. 2PECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - In Exercises 3–18, find values of the...Ch. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - In Exercises 19–26, find the values of the...Ch. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - In Exercises 19–26, find the values of the...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - In Exercises 27-30, each given point is on the...Ch. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.3 - Find the value of sin 12.5°.
Ch. 4.3 - Find θ if tan θ = 1.039.
Ch. 4.3 - Find the values of cot 56.4°.
Ch. 4.3 - Prob. 4PECh. 4.3 - Prob. 1ECh. 4.3 - In Example 5, change sec 27.82° to csc 27.82° and...Ch. 4.3 - In Exercises 1–4, make the given changes in the...Ch. 4.3 -
In Exercises 1–4, make the given changes in the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - In Exercises 41–44, use a calculator to verify the...Ch. 4.3 - Prob. 42ECh. 4.3 - In Exercises 41–44, use a calculator to verify the...Ch. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - In Exercises 51–54, find the values of the...Ch. 4.3 - In Exercises 51–54, find the values of the...Ch. 4.3 - In Exercises 51–54, find the values of the...Ch. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - In Exercises 55–60, solve the given problems.
The...Ch. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.4 - Prob. 1PECh. 4.4 - Prob. 2PECh. 4.4 - Prob. 3PECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 13ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 19ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 29ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - In Exercises 31–34, find the part of the triangle...Ch. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - In Exercises 35–38, find the indicated part of the...Ch. 4.4 - Prob. 37ECh. 4.4 - In Exercises 35–38, find the indicated part of the...Ch. 4.4 - Prob. 39ECh. 4.4 - In Exercises 39–42, solve the given problems.
40....Ch. 4.4 - In Exercises 39–42, solve the given problems.
41....Ch. 4.4 - Prob. 42ECh. 4.5 - Find θ if the letters in the road are 2.0 m long,...Ch. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 5ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 8ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - In Exercises 23-28, find the indicated...Ch. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - In Exercises 5–20, find the values of the...Ch. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - In Exercises 29–36, find the values of the...Ch. 4 - In Exercises 29–36, find the values of the...Ch. 4 - Prob. 36RECh. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - Prob. 38RECh. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - In Exercises 49 and 50, assume θ is an acute angle...Ch. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - In Exercises 51–60, solve the right triangles with...Ch. 4 - In Exercises 51–60, solve the right triangles with...Ch. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 -
In Exercises 61–105, solve the given...Ch. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - The apparent power S in an electric circuit in...Ch. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 93RECh. 4 - Prob. 94RECh. 4 - Prob. 95RECh. 4 - Prob. 96RECh. 4 - Prob. 97RECh. 4 - Prob. 98RECh. 4 - Prob. 99RECh. 4 - In Exercises 61–105, solve the given...Ch. 4 - Prob. 101RECh. 4 - Prob. 102RECh. 4 - Prob. 103RECh. 4 - Prob. 104RECh. 4 - In Exercises 61–105, solve the given...Ch. 4 - Prob. 1PTCh. 4 - Prob. 2PTCh. 4 - Prob. 3PTCh. 4 - Prob. 4PTCh. 4 - Prob. 5PTCh. 4 - Find tan θ in fractional form if (assume θ is...Ch. 4 - Find csc θ if tan θ = 1.294 (assume θ is acute).
Ch. 4 - Prob. 8PTCh. 4 - Prob. 9PTCh. 4 - Prob. 10PTCh. 4 - Prob. 11PTCh. 4 - Prob. 12PTCh. 4 - Prob. 13PTCh. 4 - Prob. 14PTCh. 4 - Prob. 15PT
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