Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 9, Problem 19P
Three masses are suspended vertically by a series of identical springs where mass 1 is at the top and mass 3 is at the bottom. If
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Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
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Chapter 9 Solutions
Numerical Methods for Engineers
Ch. 9 - (a) Write the following set of equations in matrix...Ch. 9 - A number of matrices are defined as...Ch. 9 - Three matrices are defined as...Ch. 9 - Use the graphical method to solve...Ch. 9 - 9.5 Given the system of equations
(a) Solve...Ch. 9 - 9.6 For the set of equations
(a) Compute the...Ch. 9 - Given the equations 0.5x1x2=9.51.02x12x2=18.8 (a)...Ch. 9 - Given the equations...Ch. 9 - Use Gauss elimination to solve:...Ch. 9 - Given the system of equations...
Ch. 9 - 9.11 Given the equations
(a) Solve by Gauss...Ch. 9 - Use Gauss-Jordan elimination to solve:...Ch. 9 - 9.13 Solve:
with (a) naive Gauss elimination,...Ch. 9 - 9.14 Perform the same computation as in Example...Ch. 9 - 9.15 Solve
Ch. 9 - 9.16 Develop, debug, and test a program in either...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - 9.19 Three masses are suspended vertically by a...Ch. 9 - 9.20 Develop, debug, and test a program in either...Ch. 9 - 9.21 Recall from Sec. 8.2 that determining the...
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