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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Diagonalize the matrix A = [6 -2; 2 2].
💡 Hint: Calculate the eigenvalues first.
Question 2
Easy
Find the eigenvalues of the matrix A = [1 1; 0 1].
💡 Hint: Use the characteristic polynomial.
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 the form of a diagonalized matrix?
- PDP-1
- DP-P1
- PDP^-1
💡 Hint: Remember the relationship between the matrices.
Question 2
True or False: All symmetric matrices are diagonalizable.
- True
- False
💡 Hint: Consider the properties of symmetric matrices.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a matrix A = [3 1; 0 3], prove its non-diagonalizability.
💡 Hint: Examine the eigenspace to conclude.
Question 2
A symmetric matrix B = [2 1; 1 2] is given, find its eigenvalues and eigenvectors analytically.
💡 Hint: Use the characteristic polynomial to derive eigenvalues.
Challenge and get performance evaluation