Student's Solutions Manual for Fundamentals of Differential Equations and Fundamentals of Differential Equations and Boundary Value Problems
9th Edition
ISBN: 9780321977212
Author: Nagle, R. Kent; Saff, Edward B.; Snider, Arthur David
Publisher: PEARSON
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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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of 2
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ZOOM +
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 3 Solutions
Student's Solutions Manual for Fundamentals of Differential Equations and Fundamentals of Differential Equations and Boundary Value Problems
Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - A swimming pool whose volume is 10,000 gal...Ch. 3.2 - The air in a small room 12 ft by 8 ft by 8 ft is...Ch. 3.2 - Prob. 7ECh. 3.2 - A tank initially contains s0 lb of salt dissolved...Ch. 3.2 - In 1990 the Department of Natural Resources...Ch. 3.2 - Use a sketch of the phase line (see Project B,...
Ch. 3.2 - Use a sketch of the phase line (see Project B,...Ch. 3.2 - Prob. 12ECh. 3.2 - In Problem 9, suppose we have the additional...Ch. 3.2 - Prob. 14ECh. 3.2 - In Problem 14, suppose we have the additional...Ch. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Using the U.S. census data in Table 3.1 for 1900,...Ch. 3.2 - The initial mass of a certain species of fish is 7...Ch. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.3 - A cup of hot coffee initially at 95C cools to 80C...Ch. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - It was noon on a cold December day in Tampa: 16C....Ch. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Early Monday morning, the temperature in the...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - When an object slides on a surface, it encounters...Ch. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Escape Velocity. According to Newtons law of...Ch. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - The power generated or dissipated by a circuit...Ch. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - A 108-F capacitor (10 nanofarads) is charged to 50...Ch. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - In many of the following problems, it will be...Ch. 3.6 - In Exercises 13-18, use a calculator or a computer...Ch. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.7 - Prob. 1ECh. 3.7 - Prob. 2ECh. 3.7 - As in Exercises 3.6, for some problems you will...Ch. 3.7 - As in Exercises 3.6, for some problems you will...Ch. 3.7 - Prob. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - As in Exercises 3.6, for some problems you will...Ch. 3.7 - Prob. 12ECh. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - Prob. 17ECh. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21E
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