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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the characteristic equation of the matrix A = [[4, 1], [0, 4]]?
💡 Hint: Remember, I is the identity matrix.
Question 2
Easy
What is an eigenvalue?
💡 Hint: Think about how eigenvalues relate to transformations.
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 the characteristic equation tell us?
- Determines eigenvalues
- Finds determinants
- Calculates traces
💡 Hint: Focus on how the term 'characteristic' relates to eigenvalues.
Question 2
True or False: The eigenspace dimension is always equal to the algebraic multiplicity of the eigenvalue.
- True
- False
💡 Hint: Review the definitions of AM and GM.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a new matrix B = [[4, 2], [0, 4]], calculate its eigenvalues and explain if it is diagonalizable.
💡 Hint: Check the relationship between AM and GM.
Question 2
Suppose a matrix has real eigenvalues and the calculation reveals three linearly independent eigenvectors. What can be said about its diagonalizability?
💡 Hint: Recall the definition of diagonalizability.
Challenge and get performance evaluation