APM3700 Assignment 3 (COMPLETE ANSWERS) 2024 - DUE 28 August 2024 ; 100% TRUSTED Complete, trusted solutions and explanationsEnsure your success with us..

APM3700
Assignment 3
(COMPLETE
ANSWERS)
2024 - DUE 28
August 2024
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, Exam (elaborations)
APM3700 Assignment 3 (COMPLETE ANSWERS) 2024 -
DUE 28 August 2024
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 Course
 Differential Equations (APM3700)
 Institution
 University Of South Africa (Unisa)
 Book
 Engineering Differential Equations

APM3700 Assignment 3 (COMPLETE ANSWERS) 2024 - DUE 28 August
2024 ; 100% TRUSTED Complete, trusted solutions and explanationsEnsure
your success with us..



QUESTION 1 If       3 6 1 4 B , find the eigenvalues of B. (5)
QUESTION 2 If          3 2 2 0 2 1 0 0 4 A , find an eigenvector
corresponding to the eigenvalue   2 . (5) QUESTION 3 Find the
eigenvalues of           1 2 0 1 2 1 0 0 4 A and an eigenvector
corresponding to   0 . (10) QUESTION 4 Solve the following system of
linear equations by Gaussian elimination:       1 2 3 1 2 3 1 2 3 4 6 2 1 2
4323258

Question 1: Finding the Eigenvalues of Matrix BBB

We are given the matrix B=(3614)B = \begin{pmatrix} 3 & 6 \\ 1 & 4 \end{pmatrix}B=(3164).
To find the eigenvalues, we follow these steps:

1. Set Up the Characteristic Equation: The eigenvalues are the solutions to the equation: