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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a diagonal matrix.
💡 Hint: Think about where non-zero elements can be placed in the matrix.
Question 2
Easy
What is an eigenvalue?
💡 Hint: Consider what happens to an eigenvector when a linear transformation is applied.
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 diagonal matrix?
- A matrix with all elements zero
- Non-zero elements only along the diagonal
- All non-diagonal elements are non-zero
💡 Hint: Think about where you can find numbers in a diagonal matrix.
Question 2
True or False: A matrix with repeated eigenvalues is always diagonalizable.
- True
- False
💡 Hint: Consider what happens when there are fewer eigenvectors than algebraic multiplicities.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [3, 2; 4, 5], diagonalize it if possible. Show all steps.
💡 Hint: Start with finding the characteristic polynomial.
Question 2
Determine whether the matrix B = [1, 0; 0, 1] can be diagonalized. Explain why or why not.
💡 Hint: What do you notice about the form of this matrix?
Challenge and get performance evaluation