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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define geometric multiplicity.
💡 Hint: Think about the vectors corresponding to that eigenvalue.
Question 2
Easy
What is algebraic multiplicity?
💡 Hint: Look at 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 defines geometric multiplicity?
💡 Hint: Think about independent vectors corresponding to eigenvalues.
Question 2
True or False: The geometric multiplicity of an eigenvalue is always greater than its algebraic multiplicity.
- True
- False
💡 Hint: Check the definitions of both multiplicities.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A 3x3 matrix has an eigenvalue λ = 4 that appears twice in its characteristic polynomial. Determine the possible geometric multiplicities and discuss von implications on diagonalization.
💡 Hint: Think about the definitions of multiplicities in regards to independence.
Question 2
Consider the matrix A = [[1, 1], [0, 1]]. Calculate the eigenvalues, their multiplicities and determine if A is diagonalizable.
💡 Hint: Calculate the characteristic polynomial and confirm the case.
Challenge and get performance evaluation