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

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  • Course
  • Mathematics III
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  • University Of South Africa
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  • Engineering Mathematics - III

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

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




ADMIN
[COMPANY NAME]

, MAT3700 Assignment 3 (COMPLETE ANSWERS)2024 -
DUE 28 August 2024 ; 100% TRUSTED Complete, trusted
solutions and explanations.
QUESTION 1 If   =    3 6 1 4 B , find the eigenvalues of B.
(5)

To find the eigenvalues of the matrix BBB, you need to solve
the characteristic equation det(B−λI)=0\text{det}(B - \lambda I)
= 0det(B−λI)=0, where III is the identity matrix and λ\lambdaλ
represents the eigenvalues.
Given the matrix BBB:
B=(3614)B = \begin{pmatrix} 3 & 6 \\ 1 & 4
\end{pmatrix}B=(3164)
1. Form the matrix B−λIB - \lambda IB−λI:
B−λI=(3614)−λ(1001)=(3−λ614−λ)B - \lambda I =
\begin{pmatrix} 3 & 6 \\ 1 & 4 \end{pmatrix} - \lambda
\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} =
\begin{pmatrix} 3 - \lambda & 6 \\ 1 & 4 - \lambda
\end{pmatrix}B−λI=(3164)−λ(1001)=(3−λ164−λ)
2. Find the determinant of B−λIB - \lambda IB−λI:
The determinant of B−λIB - \lambda IB−λI is:
det(B−λI)=det(3−λ614−λ)\text{det}(B - \lambda I) = \text{det}
\begin{pmatrix} 3 - \lambda & 6 \\ 1 & 4 - \lambda
\end{pmatrix}det(B−λI)=det(3−λ164−λ)
To calculate the determinant:

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