21.6.2 - Finding Eigenvalues
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Practice Questions
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Define what an eigenvalue is.
💡 Hint: Think about the equation Av = λv.
What is the first step in finding eigenvalues?
💡 Hint: You will need the identity matrix.
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Interactive Quizzes
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What is the characteristic equation used to find eigenvalues?
💡 Hint: Check how we form the matrix with λ and the identity.
Eigenvalues can be complex numbers.
💡 Hint: Think about transformations in two-dimensional spaces.
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Challenge Problems
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Given a matrix B = [[1, 2], [2, 1]], calculate its eigenvalues and explain their significance.
💡 Hint: Remember to compute the determinant and find the roots.
Consider the matrix C = [[0, 2], [-1, 0]]. Find the eigenvalues and describe what they indicate about the system.
💡 Hint: Use the characteristic equation to analyze the matrix.
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