Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is an eigenvalue?
💡 Hint: Think about how eigenvalues relate to the actions on eigenvectors.
Question 2
Easy
How do you determine if a matrix is diagonalizable?
💡 Hint: Remember what you learned about linear independence.
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
A matrix is diagonalizable if it has:
- At least one eigenvalue
- n linearly independent eigenvectors
- Only distinct eigenvalues
💡 Hint: Focus on the number of eigenvectors needed.
Question 2
True or False: A matrix can be diagonalized if its eigenvalue has an algebraic multiplicity greater than its geometric multiplicity.
- True
- False
💡 Hint: Think about the definitions of both multiplicities.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the matrix [[2, 0], [0, 2]] is diagonalizable.
💡 Hint: Calculate the eigenvalues first and verify independence.
Question 2
Given the matrix [[0, 1], [0, 0]], discuss whether it can be diagonalized and justify.
💡 Hint: Remember to check the eigenvectors corresponding to the eigenvalue.
Challenge and get performance evaluation