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 eigenvector?
💡 Hint: Remember that `λ` is the eigenvalue.
Question 2
Easy
Define eigenspace.
💡 Hint: Think about the vectors that satisfy `Av = λv`.
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 defines an eigenvector?
- A vector that changes direction under transformation.
- A linear combination of vectors.
- A non-zero vector satisfying Av = λv.
💡 Hint: Focus on the eigenvalue equation.
Question 2
True or False: The eigenvalue's algebraic multiplicity can be greater than its geometric multiplicity.
- True
- False
💡 Hint: Remember the definitions of both types of multiplicity.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a matrix A = [[2, 1], [1, 2]], find its eigenvalues and eigenvectors. Discuss if it is diagonalizable.
💡 Hint: Remember to use the determinant for the characteristic polynomial.
Question 2
Consider a symmetric matrix B with eigenvalues 4, 4, and 2. Determine the geometric and algebraic multiplicities, and explain the implications for diagonalization.
💡 Hint: Think about how the multiplicities relate to the eigenspace dimensions.
Challenge and get performance evaluation