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 happens to an eigenvector if it is multiplied by a scalar?
💡 Hint: Think about if it stretches or shrinks.
Question 2
Easy
If a matrix has 3 distinct eigenvalues, how many linearly independent eigenvectors will it have?
💡 Hint: Remember the definition of distinct eigenvalues.
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 does it mean if eigenvectors are linearly independent?
💡 Hint: Recall the definition of linear independence.
Question 2
True or False: All eigenvectors of symmetric matrices are complex.
- True
- False
💡 Hint: Think about the properties of symmetric matrices.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a 3x3 real symmetric matrix, prove that its eigenvectors corresponding to distinct eigenvalues are orthogonal.
💡 Hint: Apply the eigenvalue equation and manipulate using the symmetry property.
Question 2
Consider a 4x4 matrix that has 4 distinct eigenvalues. How would you go about finding its eigenvectors? Discuss the method and implications for usage in scenarios such as structural analysis.
💡 Hint: Remember to check for linear independence.
Challenge and get performance evaluation