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3 cards from this section. Quick, good the night before a test.
Define an eigenvalue in your own words.
Think about how it affects a vector's length.
What does the characteristic polynomial help us find?
Consider what needs to be set to zero.
What mathematical equation is used to find eigenvalues of a matrix?
Recall how eigenvalues are defined.
Eigenvectors can only exist for real eigenvalues.
What about applications in electrical or dynamic systems?
Given a matrix A = [[4, 1, 1], [1, 3, 1], [1, 1, 2]], find its eigenvalues and eigenvectors.
Construct the determinant and remember to find the null space for vectors.
How do eigenvalues influence the design of a bridge subject to dynamic loads? Discuss.
Connect your answers with structural integrity and loading responses.
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