29.3.1 - Algebraic Multiplicity
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Practice Questions
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What is algebraic multiplicity?
💡 Hint: Consider how many times you can factor the polynomial.
Define geometric multiplicity.
💡 Hint: Think about how many directions correspond to that eigenvalue.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does algebraic multiplicity refer to?
💡 Hint: Focus on root counting!
True or False: Geometric multiplicity can be greater than algebraic multiplicity.
💡 Hint: Remember the inequalities we've discussed.
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Challenge Problems
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Consider a matrix with characteristic polynomial p(λ) = (λ - 3)³(λ - 2) = 0. Determine the algebraic and geometric multiplicities for each eigenvalue.
💡 Hint: Don't forget the concepts and check eigenspace dimensions!
If an eigenvalue's algebraic multiplicity is 5 and geometric is 3, what can you infer about the matrix properties in terms of stability?
💡 Hint: Link it back to applications in structural assessments.
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