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 27, Problem 19P
Use the Excel Solver to directly solve (that is, without linearization) Prob. 27.6 using the finite-difference approach. Employ
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
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2) Given the following matrices A =
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and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
Using Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).
Consider the alphabet {a, b, c}.• Design a regular expression that recognizes all strings over {a, b, c} that have at least three nonconsec-utive c characters (two characters are non-consecutive if there is at least one character between them)and at least one a character.• Explain how your regular expression recognizes the string cbbcccac by clearly identifying which partsof the string match to the components of your regular expression
Chapter 27 Solutions
Numerical Methods for Engineers
Ch. 27 - A steady-state heat balance for a rod can be...Ch. 27 - 27.2 Use the shooting method to solve Prob. 27.1....Ch. 27 - 27.3 Use the finite-difference approach with to...Ch. 27 - 27.4 Use the shooting method to solve
Ch. 27 - Solve Prob. 27.4 with the finite-difference...Ch. 27 - 27.7 Differential equations like the one solved...Ch. 27 - 27.8 Repeat Example 27.4 but for three masses....Ch. 27 - 27.9 Repeat Example 27.6, but for five interior...Ch. 27 - Use minors to expand the determinant of...Ch. 27 - 27.11 Use the power method to determine the...
Ch. 27 - 27.12 Use the power method to determine the...Ch. 27 - Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.13 to solve...Ch. 27 - 27.15 Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.15 to solve...Ch. 27 - 27.17 Develop a user-friendly program to solve...Ch. 27 - Develop a user-friendly program to solve for the...Ch. 27 - 27.19 Use the Excel Solver to directly solve...Ch. 27 - Use MATLAB to integrate the following pair of ODEs...Ch. 27 - The following differential equation can be used to...Ch. 27 - 27.22 Use MATLAB or Mathcad to...Ch. 27 - 27.23 Use finite differences to solve the...Ch. 27 - Solve the nondimensionalized ODE using finite...Ch. 27 - 27.25 Derive the set of differential equations for...Ch. 27 - 27.26 Consider the mass-spring system in Fig....Ch. 27 - 27.27 The following nonlinear, parasitic ODE was...Ch. 27 - A heated rod with a uniform heat source can be...Ch. 27 - 27.29 Repeat Prob. 27.28, but for the following...Ch. 27 - 27.30 Suppose that the position of a falling...Ch. 27 - Repeat Example 27.3, but insulate the left end of...
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