Practice - Diagonalization of Matrices
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Practice Questions
Test your understanding with targeted questions
Define a diagonal matrix.
💡 Hint: Think about the placement of zeroes in a matrix.
What is an eigenvector?
💡 Hint: Consider how vectors interact with linear transformations.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a diagonal matrix?
💡 Hint: Remember where zeroes are placed in such matrices.
True or False: If a matrix has repeated eigenvalues, it is always diagonalizable.
💡 Hint: Think about the conditions required for diagonalization.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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