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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 the placement of zeroes in a matrix.
Question 2
Easy
What is an eigenvector?
💡 Hint: Consider how vectors interact with linear 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 is a diagonal matrix?
- A matrix with all zero elements
- A matrix with non-zero values only on the diagonal
- A square matrix with eigenvectors
💡 Hint: Remember where zeroes are placed in such matrices.
Question 2
True or False: If a matrix has repeated eigenvalues, it is always diagonalizable.
- True
- False
💡 Hint: Think about the conditions required for diagonalization.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [[4, 1], [2, 3]], find the eigenvalues and determine whether A is diagonalizable. Justify your reasoning.
💡 Hint: Use the characteristic polynomial to derive the eigenvalues.
Question 2
For the matrix B = [[2, -1], [0, 2]], analyze the multiplicities of eigenvalues and determine its diagonalizability.
💡 Hint: Check the number of linearly independent eigenvectors compared to the eigenvalue's multiplicity.
Challenge and get performance evaluation