33.1 - Diagonalization of a Matrix
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Practice Questions
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Define a diagonal matrix.
💡 Hint: Think about where non-zero elements can be placed in the matrix.
What is an eigenvalue?
💡 Hint: Consider what happens to an eigenvector when a linear transformation is applied.
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Interactive Quizzes
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What is a diagonal matrix?
💡 Hint: Think about where you can find numbers in a diagonal matrix.
True or False: A matrix with repeated eigenvalues is always diagonalizable.
💡 Hint: Consider what happens when there are fewer eigenvectors than algebraic multiplicities.
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Challenge Problems
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Given the matrix A = [3, 2; 4, 5], diagonalize it if possible. Show all steps.
💡 Hint: Start with finding the characteristic polynomial.
Determine whether the matrix B = [1, 0; 0, 1] can be diagonalized. Explain why or why not.
💡 Hint: What do you notice about the form of this matrix?
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