21.11.2 - Conditions for Diagonalizability
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Practice Questions
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Define a diagonalizable matrix.
💡 Hint: Remember the form of the diagonal matrix.
What must a matrix have to be diagonalizable?
💡 Hint: Think about the concepts of eigenvalues and eigenvectors.
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Interactive Quizzes
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What is a necessary condition for a matrix to be diagonalizable?
💡 Hint: Think about the definitions of eigenvectors.
True or False: All matrices with distinct eigenvalues are diagonalizable.
💡 Hint: Recall how eigenvalues relate to diagonalizability.
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Challenge Problems
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Prove that the matrix A = [[1, 2], [0, 3]] is diagonalizable or not. Use computational methods to find eigenvalues and relations.
💡 Hint: Calculate eigenvalues using the characteristic polynomial.
Create a diagonalizable matrix of size 3x3 and show that it satisfies necessary diagonalizability conditions.
💡 Hint: Choose distinct eigenvalues and construct accordingly.
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