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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the minimal polynomial of a matrix?
💡 Hint: Think about polynomials and matrices.
Question 2
Easy
Does the minimal polynomial divide the characteristic polynomial?
💡 Hint: Consider how these polynomials relate to eigenvalues.
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 degree of the minimal polynomial related to?
- It is always greater than the degree of the characteristic polynomial
- It cannot be less than the degree of the characteristic polynomial
- It can be equal to or less than the degree of the characteristic polynomial
💡 Hint: Think about how polynomials relate in linear algebra.
Question 2
Is it true that the minimal polynomial must be a factor of the characteristic polynomial?
- True
- False
💡 Hint: Recall their mathematical relationship.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [[1, 2],[0, 1]], find its minimal polynomial and explain your reasoning.
💡 Hint: Calculate the eigenvalues and their multiplicities.
Question 2
If a matrix has a minimal polynomial of m(x) = (x - 3)(x - 2)^2, what can you infer about its eigenvalues and their respective multiplicities?
💡 Hint: Review the factors and their powers.
Challenge and get performance evaluation