Basic Technical Mathematics
11th Edition
ISBN: 9780134437705
Author: Washington
Publisher: PEARSON
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Chapter 19, Problem 31RE
To determine
The fraction that has the decimal form
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Let
2
A =
4
3
-4
0
1
(a) Show that v =
eigenvalue.
()
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
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
Chapter 19 Solutions
Basic Technical Mathematics
Ch. 19.1 - Find the 20th term of the arithmetic sequence 2,...Ch. 19.1 - Prob. 2PECh. 19.1 - Prob. 3PECh. 19.1 - Prob. 1ECh. 19.1 - Prob. 2ECh. 19.1 - Prob. 3ECh. 19.1 - Prob. 4ECh. 19.1 - In Exercises 3–6, write the first five terms of...Ch. 19.1 - Prob. 6ECh. 19.1 - Prob. 7E
Ch. 19.1 - Prob. 8ECh. 19.1 - Prob. 9ECh. 19.1 - In Exercises 7–14, find the nth term of the...Ch. 19.1 - Prob. 11ECh. 19.1 - Prob. 12ECh. 19.1 - Prob. 13ECh. 19.1 - Prob. 14ECh. 19.1 - In Exercises 15–18, find the sum of the n terms of...Ch. 19.1 - Prob. 16ECh. 19.1 - Prob. 17ECh. 19.1 - Prob. 18ECh. 19.1 - Prob. 19ECh. 19.1 - Prob. 20ECh. 19.1 - Prob. 21ECh. 19.1 - Prob. 22ECh. 19.1 - Prob. 23ECh. 19.1 - Prob. 24ECh. 19.1 - Prob. 25ECh. 19.1 - Prob. 26ECh. 19.1 - In Exercises 27–56, find the indicated quantities...Ch. 19.1 - Prob. 28ECh. 19.1 - Prob. 29ECh. 19.1 - Prob. 30ECh. 19.1 - In Exercises 27–56, find the indicated quantities...Ch. 19.1 - Prob. 32ECh. 19.1 - Prob. 33ECh. 19.1 - Prob. 34ECh. 19.1 - Prob. 35ECh. 19.1 - Prob. 36ECh. 19.1 - Prob. 37ECh. 19.1 - Prob. 38ECh. 19.1 - Prob. 39ECh. 19.1 - Prob. 40ECh. 19.1 - Prob. 41ECh. 19.1 - In Exercises 27–56, find the indicated quantities...Ch. 19.1 - Prob. 43ECh. 19.1 - In Exercises 27–56, find the indicated quantities...Ch. 19.1 - Prob. 45ECh. 19.1 - Prob. 46ECh. 19.1 - Prob. 47ECh. 19.1 - Prob. 48ECh. 19.1 - In Exercises 27–56, find the indicated quantities...Ch. 19.1 - Prob. 50ECh. 19.1 - Prob. 51ECh. 19.1 -
In Exercises 27–56, find the indicated quantities...Ch. 19.1 - Prob. 53ECh. 19.1 - Prob. 54ECh. 19.1 - Prob. 55ECh. 19.1 - Prob. 56ECh. 19.2 -
Find the sixth term of the geometric sequence 8,...Ch. 19.2 - Prob. 2PECh. 19.2 - Prob. 3PECh. 19.2 - Prob. 1ECh. 19.2 - Prob. 2ECh. 19.2 - Prob. 3ECh. 19.2 - Prob. 4ECh. 19.2 - Prob. 5ECh. 19.2 - Prob. 6ECh. 19.2 - Prob. 7ECh. 19.2 - Prob. 8ECh. 19.2 - Prob. 9ECh. 19.2 - Prob. 10ECh. 19.2 - Prob. 11ECh. 19.2 - Prob. 12ECh. 19.2 - Prob. 13ECh. 19.2 - Prob. 14ECh. 19.2 - In Exercises 15–20, find the sum of the first n...Ch. 19.2 - Prob. 16ECh. 19.2 - Prob. 17ECh. 19.2 - Prob. 18ECh. 19.2 - Prob. 19ECh. 19.2 - Prob. 20ECh. 19.2 - Prob. 21ECh. 19.2 - Prob. 22ECh. 19.2 -
In Exercises 21–28, find any of the values of a1,...Ch. 19.2 - Prob. 24ECh. 19.2 -
In Exercises 21–28, find any of the values of a1,...Ch. 19.2 - Prob. 26ECh. 19.2 - Prob. 27ECh. 19.2 - Prob. 28ECh. 19.2 - Prob. 29ECh. 19.2 - Prob. 30ECh. 19.2 - Prob. 31ECh. 19.2 - Prob. 32ECh. 19.2 - Prob. 33ECh. 19.2 - Prob. 34ECh. 19.2 - Prob. 35ECh. 19.2 - Prob. 36ECh. 19.2 - Prob. 37ECh. 19.2 - Prob. 38ECh. 19.2 - Prob. 39ECh. 19.2 - Prob. 40ECh. 19.2 - Prob. 41ECh. 19.2 - Prob. 42ECh. 19.2 - Prob. 43ECh. 19.2 - Prob. 44ECh. 19.2 - Prob. 45ECh. 19.2 - Prob. 46ECh. 19.2 - Prob. 47ECh. 19.2 - Prob. 48ECh. 19.2 - Prob. 49ECh. 19.2 - Prob. 50ECh. 19.2 -
In Exercises 29–56, find the indicated...Ch. 19.2 - Prob. 52ECh. 19.2 -
In Exercises 29–56, find the indicated...Ch. 19.2 - Prob. 54ECh. 19.2 -
In Exercises 29–56, find the indicated...Ch. 19.2 - Prob. 56ECh. 19.3 - Prob. 1PECh. 19.3 - Prob. 2PECh. 19.3 - Prob. 3PECh. 19.3 - Prob. 1ECh. 19.3 - Prob. 2ECh. 19.3 - Prob. 3ECh. 19.3 - Prob. 4ECh. 19.3 - Prob. 5ECh. 19.3 - Prob. 6ECh. 19.3 - Prob. 7ECh. 19.3 - Prob. 8ECh. 19.3 - Prob. 9ECh. 19.3 - Prob. 10ECh. 19.3 - Prob. 11ECh. 19.3 - Prob. 12ECh. 19.3 - Prob. 13ECh. 19.3 - Prob. 14ECh. 19.3 - Prob. 15ECh. 19.3 - Prob. 16ECh. 19.3 - Prob. 17ECh. 19.3 - Prob. 18ECh. 19.3 - In Exercises 15–24, find the fractions equal to...Ch. 19.3 - In Exercises 15–24, find the fractions equal to...Ch. 19.3 - Prob. 21ECh. 19.3 - Prob. 22ECh. 19.3 - Prob. 23ECh. 19.3 - Prob. 24ECh. 19.3 - Prob. 25ECh. 19.3 - Prob. 26ECh. 19.3 - Prob. 27ECh. 19.3 - In Exercises 25–36, solve the given problems by...Ch. 19.3 - Prob. 29ECh. 19.3 - Prob. 30ECh. 19.3 - Prob. 31ECh. 19.3 - Prob. 32ECh. 19.3 - Prob. 33ECh. 19.3 - Prob. 34ECh. 19.3 - Prob. 35ECh. 19.3 - Prob. 36ECh. 19.4 - Prob. 1PECh. 19.4 - Prob. 2PECh. 19.4 - Prob. 3PECh. 19.4 - Prob. 4PECh. 19.4 - Prob. 1ECh. 19.4 - Prob. 2ECh. 19.4 - Prob. 3ECh. 19.4 - Prob. 4ECh. 19.4 - Prob. 5ECh. 19.4 - Prob. 6ECh. 19.4 - Prob. 7ECh. 19.4 - Prob. 8ECh. 19.4 - Prob. 9ECh. 19.4 - Prob. 10ECh. 19.4 - Prob. 11ECh. 19.4 - Prob. 12ECh. 19.4 - Prob. 13ECh. 19.4 - Prob. 14ECh. 19.4 - Prob. 15ECh. 19.4 - Prob. 16ECh. 19.4 - Prob. 17ECh. 19.4 - Prob. 18ECh. 19.4 - Prob. 19ECh. 19.4 - Prob. 20ECh. 19.4 - Prob. 21ECh. 19.4 - Prob. 22ECh. 19.4 - Prob. 23ECh. 19.4 - Prob. 24ECh. 19.4 - Prob. 25ECh. 19.4 - Prob. 26ECh. 19.4 - Prob. 27ECh. 19.4 - Prob. 28ECh. 19.4 - Prob. 29ECh. 19.4 - Prob. 30ECh. 19.4 - Prob. 31ECh. 19.4 - Prob. 32ECh. 19.4 - Prob. 33ECh. 19.4 - Prob. 34ECh. 19.4 - Prob. 35ECh. 19.4 - Prob. 36ECh. 19.4 - Prob. 37ECh. 19.4 - Prob. 38ECh. 19.4 - Prob. 39ECh. 19.4 - Prob. 40ECh. 19.4 - Prob. 41ECh. 19.4 - Prob. 42ECh. 19.4 - Prob. 43ECh. 19.4 - Prob. 44ECh. 19.4 - Prob. 45ECh. 19.4 - Prob. 46ECh. 19.4 - Prob. 47ECh. 19.4 - Prob. 48ECh. 19.4 - Prob. 49ECh. 19.4 - Prob. 50ECh. 19.4 - Prob. 51ECh. 19.4 - Prob. 52ECh. 19.4 - Prob. 53ECh. 19.4 - Prob. 54ECh. 19.4 - Prob. 55ECh. 19.4 - Prob. 56ECh. 19.4 - In Exercises 45–58, solve the given problems.
57....Ch. 19.4 - Prob. 58ECh. 19 - Prob. 1RECh. 19 - Prob. 2RECh. 19 - Prob. 3RECh. 19 - Prob. 4RECh. 19 - Prob. 5RECh. 19 - Prob. 6RECh. 19 - Prob. 7RECh. 19 - Prob. 8RECh. 19 - Prob. 9RECh. 19 - Prob. 10RECh. 19 - Prob. 11RECh. 19 - Prob. 12RECh. 19 - Prob. 13RECh. 19 - Prob. 14RECh. 19 - Prob. 15RECh. 19 - Prob. 16RECh. 19 - Prob. 17RECh. 19 - Prob. 18RECh. 19 - Prob. 19RECh. 19 - Prob. 20RECh. 19 - Prob. 21RECh. 19 - Prob. 22RECh. 19 - Prob. 23RECh. 19 - Prob. 24RECh. 19 - Prob. 25RECh. 19 - Prob. 26RECh. 19 - Prob. 27RECh. 19 - Prob. 28RECh. 19 - In Exercises 27–30, find the sums of the given...Ch. 19 - Prob. 30RECh. 19 - Prob. 31RECh. 19 - Prob. 32RECh. 19 - In Exercises 31–34, find the fractions equal to...Ch. 19 - Prob. 34RECh. 19 - Prob. 35RECh. 19 - Prob. 36RECh. 19 - Prob. 37RECh. 19 - Prob. 38RECh. 19 - Prob. 39RECh. 19 - Prob. 40RECh. 19 - Prob. 41RECh. 19 - Prob. 42RECh. 19 - Prob. 43RECh. 19 - Prob. 44RECh. 19 - Prob. 45RECh. 19 - Prob. 46RECh. 19 - Prob. 47RECh. 19 - Prob. 48RECh. 19 - Prob. 49RECh. 19 - Prob. 50RECh. 19 - Prob. 51RECh. 19 - Prob. 52RECh. 19 - Prob. 53RECh. 19 - Prob. 54RECh. 19 - Prob. 55RECh. 19 - Prob. 56RECh. 19 - Prob. 57RECh. 19 - Prob. 58RECh. 19 - Prob. 59RECh. 19 - Prob. 60RECh. 19 - Prob. 61RECh. 19 - Prob. 62RECh. 19 - Prob. 63RECh. 19 - Prob. 64RECh. 19 - Prob. 65RECh. 19 - Prob. 66RECh. 19 - Prob. 67RECh. 19 - Prob. 68RECh. 19 - In Exercises 51–98, solve the given problems by...Ch. 19 - Prob. 70RECh. 19 - Prob. 71RECh. 19 - Prob. 72RECh. 19 - Prob. 73RECh. 19 - Prob. 74RECh. 19 - Prob. 75RECh. 19 - Prob. 76RECh. 19 - Prob. 77RECh. 19 - Prob. 78RECh. 19 - Prob. 79RECh. 19 - Prob. 80RECh. 19 - In Exercises 51–98, solve the given problems by...Ch. 19 - Prob. 82RECh. 19 - Prob. 83RECh. 19 - Prob. 84RECh. 19 - Prob. 85RECh. 19 - Prob. 86RECh. 19 - Prob. 87RECh. 19 - Prob. 88RECh. 19 - In Exercises 51–98, solve the given problems by...Ch. 19 - Prob. 90RECh. 19 - Prob. 91RECh. 19 - Prob. 92RECh. 19 - Prob. 93RECh. 19 - Prob. 94RECh. 19 - Prob. 95RECh. 19 - Prob. 96RECh. 19 - Prob. 97RECh. 19 - Prob. 98RECh. 19 - Prob. 99RECh. 19 - Prob. 1PTCh. 19 - Prob. 2PTCh. 19 - Prob. 3PTCh. 19 - Prob. 4PTCh. 19 - Prob. 5PTCh. 19 - Prob. 6PTCh. 19 - Prob. 7PTCh. 19 - Prob. 8PTCh. 19 - Prob. 9PT
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