Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 13, Problem 7P
Consider the following function:
Use analytical and graphical methods to show the function has a maximum for some value of x in the range
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Please help solve the following whilst showing all working out. Is part of exam revision questions but no solution is given
please help me with this question with working out thanks
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1
of 2
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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
01
-2
3
2) Given the following matrices A =
-1
0
1] an
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.
Chapter 13 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 13 - 13.1 Given the formula
(a) Determine the...Ch. 13 - 13.2 Given
(a) Plot the function.
(b) Use...Ch. 13 - Prob. 3PCh. 13 - Repeat Prob. 13.3, except use parabolic...Ch. 13 - 13.5 Repeat Prob. 13.3 but use Newton’s method....Ch. 13 - Employ the following methods to find the maximum...Ch. 13 - 13.7 Consider the following function:
Use...Ch. 13 - Employ the following methods to find the maximum...Ch. 13 - 13.9 Consider the following function:
Perform...Ch. 13 - Consider the following function:...
Ch. 13 - 13.11 Determine the minimum of the function from...Ch. 13 - Develop a program using a programming or macro...Ch. 13 - Develop a program as described in Prob. 13.12, but...Ch. 13 - 13.14 Develop a program using a programming or...Ch. 13 - 13.15 Develop a program using a programming or...Ch. 13 - Pressure measurements are taken at certain points...Ch. 13 - 13.17 The trajectory of a ball can be computed...Ch. 13 - 13.18 The deflection of a uniform beam subject to...Ch. 13 - An object with a mass of 100 kg is projected...Ch. 13 - The normal distribution is a bell-shaped curve...Ch. 13 - An object can be projected upward at a specified...Ch. 13 - Use the golden-section search to determine the...
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