Practice Finding Eigenvalues (21.6.2) - Linear Algebra - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Define what an eigenvalue is.
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Think about the equation Av = λv.
Question 2.
What is the first step in finding eigenvalues?
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You will need the identity matrix.
3Question 3.
What is the characteristic equation used to find eigenvalues?
- det(A + λI) = 0
- det(A - λI) = 0
- det(A - I) = 0
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Check how we form the matrix with λ and the identity.
4Question 4.
Eigenvalues can be complex numbers.
- True
- False
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Think about transformations in two-dimensional spaces.
Question 5.
Given a matrix B = [[1, 2], [2, 1]], calculate its eigenvalues and explain their significance.
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Remember to compute the determinant and find the roots.
Question 6.
Consider the matrix C = [[0, 2], [-1, 0]]. Find the eigenvalues and describe what they indicate about the system.
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Use the characteristic equation to analyze the matrix.

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