32.9 - Summary of Key Concepts
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Practice Questions
Test your understanding with targeted questions
Define an eigenspace in your own words.
💡 Hint: Think about what null space means in context.
What does it mean for a matrix to be diagonalizable?
💡 Hint: Focus on how matrices can be expressed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What represents the null space of (A - λI)?
💡 Hint: Consider the definition of eigenspaces.
True or False: A matrix can be diagonalizable with fewer than n eigenvectors.
💡 Hint: Reflect on the definition of diagonalizable matrices.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given the matrix A = [[2, 0], [0, 3]], find its eigenvalues and check if A is diagonalizable.
💡 Hint: Calculate the eigenvalues and check the linear independence of the eigenvectors.
Consider a 3x3 matrix with eigenvalues of 1, 1, and 2. Determine if it's diagonalizable.
💡 Hint: Check the geometric vs algebraic multiplicity for eigenvalues.
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