33.7 - Non-Diagonalizable Matrices and Jordan Form (Brief Note)
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Practice Questions
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What makes a matrix non-diagonalizable?
💡 Hint: Consider the relationship between eigenvalues and eigenvectors.
Describe how Jordan form can be useful for studying non-diagonalizable matrices.
💡 Hint: Think about how block structures can help with computations.
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Interactive Quizzes
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What is the Jordan form used for?
💡 Hint: Think about what you do when diagonalization fails.
True or False: All matrices in civil engineering are diagonalizable.
💡 Hint: Consider the definitions we've discussed.
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Challenge Problems
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For the matrix A = [1 1; 0 1], determine if it is diagonalizable. If not, describe its Jordan form.
💡 Hint: Check the algebraic and geometric multiplicities and how they relate.
Find a non-diagonalizable matrix of size 3 and explain its Jordan form.
💡 Hint: Consider how repeated eigenvalues lead to Jordan blocks.
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