Practice - Example
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Practice Questions
Test your understanding with targeted questions
What is the characteristic equation of the matrix A = [[4, 1], [0, 4]]?
💡 Hint: Remember, I is the identity matrix.
What is an eigenvalue?
💡 Hint: Think about how eigenvalues relate to transformations.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the characteristic equation tell us?
💡 Hint: Focus on how the term 'characteristic' relates to eigenvalues.
True or False: The eigenspace dimension is always equal to the algebraic multiplicity of the eigenvalue.
💡 Hint: Review the definitions of AM and GM.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a new matrix B = [[4, 2], [0, 4]], calculate its eigenvalues and explain if it is diagonalizable.
💡 Hint: Check the relationship between AM and GM.
Suppose a matrix has real eigenvalues and the calculation reveals three linearly independent eigenvectors. What can be said about its diagonalizability?
💡 Hint: Recall the definition of diagonalizability.
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