Practice Finding Eigenvectors (21.6.3) - Linear Algebra - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Define eigenvector.
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Consider how transformations affect direction and size.
Question 2.
What does the characteristic equation determine?
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Think about how this relates to the matrix's properties.
3Question 3.
What does an eigenvector represent in matrix transformations?
- It is always zero
- It changes direction
- It scales by a factor
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Remember, they don’t rotate under transformation.
4Question 4.
The characteristic equation is used to find:
- True
- False
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Think about the properties that define eigenvalues.
Question 5.
Given the matrix A = [[2, 1], [1, 2]], find the eigenvalues and corresponding eigenvectors.
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Start with determinants and remember to substitute for eigenvalues.
Question 6.
In structural engineering, explain the role of eigenvectors in analyzing the stability of a cantilever beam.
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Reflect on vibration and structural response under load.

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