Practice - Practice Problems
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Practice Questions
Test your understanding with targeted questions
Diagonalize the matrix A = [6 -2; 2 2].
💡 Hint: Calculate the eigenvalues first.
Find the eigenvalues of the matrix A = [1 1; 0 1].
💡 Hint: Use the characteristic polynomial.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the form of a diagonalized matrix?
💡 Hint: Remember the relationship between the matrices.
True or False: All symmetric matrices are diagonalizable.
💡 Hint: Consider the properties of symmetric matrices.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a matrix A = [3 1; 0 3], prove its non-diagonalizability.
💡 Hint: Examine the eigenspace to conclude.
A symmetric matrix B = [2 1; 1 2] is given, find its eigenvalues and eigenvectors analytically.
💡 Hint: Use the characteristic polynomial to derive eigenvalues.
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