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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean for a matrix to be diagonalizable?
💡 Hint: Consider what forms the P and D matrices take.
Question 2
Easy
Define eigenvector in your own words.
💡 Hint: Think about how vectors behave under matrix multiplication.
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 a diagonalizable matrix?
- A matrix with all zero eigenvalues
- A matrix that can be expressed as A = PDP⁻¹
- A matrix that is only square
💡 Hint: Think about the definition provided earlier.
Question 2
True or False: The diagonal matrix D only contains elements on its diagonal.
- True
- False
💡 Hint: Remember the definition of a diagonal matrix.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a matrix A = [[4, 1], [1, 4]], find if it is diagonalizable, and if so, compute the diagonalized form.
💡 Hint: Start by finding the characteristic polynomial to determine eigenvalues.
Question 2
If a system of differential equations can be expressed in matrix form as dx/dt = Ax, how would diagonalization of A assist in solving this system?
💡 Hint: Consider how each eigenvalue influences the shape of the solution curve.
Challenge and get performance evaluation