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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define an eigenspace in your own words.
💡 Hint: Think about what null space means in context.
Question 2
Easy
What does it mean for a matrix to be diagonalizable?
💡 Hint: Focus on how matrices can be expressed.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What represents the null space of (A - λI)?
- Eigenvectors
- Eigenvalues
- Eigenspaces
💡 Hint: Consider the definition of eigenspaces.
Question 2
True or False: A matrix can be diagonalizable with fewer than n eigenvectors.
- True
- False
💡 Hint: Reflect on the definition of diagonalizable matrices.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation