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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of an eigenvalue?
💡 Hint: Think of the transformation of vectors.
Question 2
Easy
How do you find eigenvalues for a matrix?
💡 Hint: Calculate the determinant and set it to zero.
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 an eigenvalue represent?
- A vector that changes direction
- A scalar that indicates scaling of an eigenvector
- A constant value of the matrix
💡 Hint: Think about what happens when a vector is transformed.
Question 2
The equation Av = λv is used to define which concept?
- True
- False
💡 Hint: Recall the definition of eigenvalues and eigenvectors.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix B = [[5, 4], [0, 2]], find its eigenvalues and eigenvectors, and discuss its diagonalizability.
💡 Hint: Start with the characteristic equation.
Question 2
Consider the matrix C = [[1, 1], [0, 1]]. Investigate if it's diagonalizable and explain why or why not.
💡 Hint: Check the multiplicities!
Challenge and get performance evaluation