33.2 - Eigenvalues and Eigenvectors Review
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Practice Questions
Test your understanding with targeted questions
What is the definition of an eigenvalue?
💡 Hint: Think of the transformation of vectors.
How do you find eigenvalues for a matrix?
💡 Hint: Calculate the determinant and set it to zero.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does an eigenvalue represent?
💡 Hint: Think about what happens when a vector is transformed.
The equation Av = λv is used to define which concept?
💡 Hint: Recall the definition of eigenvalues and eigenvectors.
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Challenge Problems
Push your limits with advanced challenges
Given the matrix B = [[5, 4], [0, 2]], find its eigenvalues and eigenvectors, and discuss its diagonalizability.
💡 Hint: Start with the characteristic equation.
Consider the matrix C = [[1, 1], [0, 1]]. Investigate if it's diagonalizable and explain why or why not.
💡 Hint: Check the multiplicities!
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