Practice Eigenvalues And Eigenvectors (29.1.1) - Eigenvalues

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6 sample questions

Question 1.
Define eigenvalue.
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Think about the equation involving a matrix and a vector.
Question 2.
What is an eigenvector?
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Focus on the relationship between the vector and the matrix.
3Question 3.
What is the eigenvalue of a matrix?
- A moment of a vector
- A measure of structure's stiffness
- A scalar associated with a matrix transformation
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Focus on the transformation equation.
4Question 4.
True or False: An eigenvector can be the zero vector.
- True
- False
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Think about the definition of eigenvectors.
Question 5.
Given matrix A = [[4, 2], [1, 3]], compute the eigenvalues and eigenvectors.
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Don't forget to substitute each λ back to find eigenvectors.
Question 6.
Discuss the implications of geometric multiplicity in real-world structures.
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Link it to how stresses distribute in materials.

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