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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what an eigenvector is.
💡 Hint: Think about how it relates to matrices and transformations.
Question 2
Easy
What does the eigenspace correspond to?
💡 Hint: Remember this definition involves the concept of null spaces.
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 an eigenvector?
💡 Hint: Think of the relationship between the vector v and the transformation A.
Question 2
An eigenvalue can have multiple corresponding eigenvectors. True or False?
💡 Hint: Recall the definition of eigenspaces.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [[2, -1], [1, 1]], find its eigenvalues and eigenvectors. Discuss the implications of your results on the matrix's diagonalizability.
💡 Hint: Focus on the steps to derive the characteristic polynomial and the eigenvectors from there.
Question 2
Explore a 3x3 matrix with one eigenvalue repeated three times but only one linearly independent eigenvector. How would you illustrate this with an example, and what does it signify?
💡 Hint: Remember to check both the characteristic polynomial and null space.
Challenge and get performance evaluation