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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a diagonalizable matrix.
💡 Hint: Remember the form of the diagonal matrix.
Question 2
Easy
What must a matrix have to be diagonalizable?
💡 Hint: Think about the concepts of eigenvalues and eigenvectors.
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 a necessary condition for a matrix to be diagonalizable?
- It has at least one zero eigenvalue
- It must have n linearly independent eigenvectors
- It must be an identity matrix
💡 Hint: Think about the definitions of eigenvectors.
Question 2
True or False: All matrices with distinct eigenvalues are diagonalizable.
- True
- False
💡 Hint: Recall how eigenvalues relate to diagonalizability.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the matrix A = [[1, 2], [0, 3]] is diagonalizable or not. Use computational methods to find eigenvalues and relations.
💡 Hint: Calculate eigenvalues using the characteristic polynomial.
Question 2
Create a diagonalizable matrix of size 3x3 and show that it satisfies necessary diagonalizability conditions.
💡 Hint: Choose distinct eigenvalues and construct accordingly.
Challenge and get performance evaluation