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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the characteristic polynomial of the matrix A = [[4, 1], [2, 3]]?
💡 Hint: Use det(A - λI) to derive it.
Question 2
Easy
Define what eigenvalues are in relation to a matrix.
💡 Hint: Think about the effect of a transformation on vectors.
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 is the significance of the characteristic polynomial in diagonalization?
- It provides eigenvalues
- It gives eigenvectors
- It's irrelevant
💡 Hint: Think about where eigenvalues come from.
Question 2
True or False: Every matrix can be diagonalized.
- True
- False
💡 Hint: Consider the conditions for diagonalizability.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [[5, 1], [2, 4]], find its eigenvalues and demonstrate the diagonalization process.
💡 Hint: Follow the characteristic polynomial and eigenvector process.
Question 2
Consider the matrix A = [[3, 2], [4, 1]]. Is it diagonalizable? Justify your answer with calculations.
💡 Hint: Always compare the algebraic and geometric multiplicities.
Challenge and get performance evaluation