MAT3700 Assignment 3 (COMPLETE ANSWERS)2024 - DUE 28 August 2024 ; 100% TRUSTED Complete, trusted solutions and explanations. Ensure your success with us..

MAT3700
Assignment 3
2024 - DUE 28
August 2024
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, Exam (elaborations)
MAT3700 Assignment 3 (COMPLETE ANSWERS)2024 -
DUE 28 August 2024
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 Course
 Mathematics III (MAT3700)
Institution

 University Of South Africa (Unisa)
 Book
 Engineering Mathematics - III

MAT3700 Assignment 3 (COMPLETE ANSWERS)2024 - DUE 28 August
2024 ; 100% TRUSTED Complete, trusted solutions and explanations. Ensure
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

Find the eigenvalues of the matrix BBB, where:

3 & 6 \\ 1 & 4 \end{bmatrix} \] **Steps:** 1. **Compute the characteristic polynomial:** The
eigenvalues are found by solving the characteristic polynomial, which is given by: \[ \text{det}
(B - \lambda I) = 0

where III is the identity matrix and λ\lambdaλ represents the eigenvalue.