32.12 - Diagonalizability and Basis of Eigenvectors
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Practice Questions
Test your understanding with targeted questions
Define diagonalizability in your own words.
💡 Hint: Consider the form A = PDP⁻¹.
What is an eigenvalue?
💡 Hint: Think about how it relates to eigenvectors in the equation Av = λv.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main condition for a matrix to be diagonalizable?
💡 Hint: Think about how many vectors are needed to span the space.
True or False: All symmetric matrices are diagonalizable.
💡 Hint: Recall the properties of symmetric matrices.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Given a 3x3 matrix with eigenvalues 2 (multiplicity 2) and 3 (multiplicity 1), explain whether it can be diagonalized and justify your answer.
💡 Hint: Explore geometric vs algebraic multiplicity.
Demonstrate the process of diagonalization for a symmetric matrix with eigenvalues 4, 5, and 6. Calculate P and D, showing all steps.
💡 Hint: Use the characteristics of symmetric matrices.
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