33.3 - Diagonalization Criteria
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Practice Questions
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What is an eigenvalue?
💡 Hint: Think about how eigenvalues relate to the actions on eigenvectors.
How do you determine if a matrix is diagonalizable?
💡 Hint: Remember what you learned about linear independence.
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Interactive Quizzes
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A matrix is diagonalizable if it has:
💡 Hint: Focus on the number of eigenvectors needed.
True or False: A matrix can be diagonalized if its eigenvalue has an algebraic multiplicity greater than its geometric multiplicity.
💡 Hint: Think about the definitions of both multiplicities.
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Challenge Problems
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Prove that the matrix [[2, 0], [0, 2]] is diagonalizable.
💡 Hint: Calculate the eigenvalues first and verify independence.
Given the matrix [[0, 1], [0, 0]], discuss whether it can be diagonalized and justify.
💡 Hint: Remember to check the eigenvectors corresponding to the eigenvalue.
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