21.6.1 - Definition
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Practice Questions
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Define what an eigenvalue is in your own words.
💡 Hint: Think about how vectors might change with a matrix.
What does it mean for a vector to be an eigenvector?
💡 Hint: Consider a vector that scales but does not rotate.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the equation for finding eigenvalues?
💡 Hint: Remember, we adjust the matrix A by subtracting λI.
True or False: Eigenvectors corresponding to distinct eigenvalues are always linearly independent.
💡 Hint: Think about the applicability of eigenvalues.
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Challenge Problems
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Given the matrix M = [[3,1],[2,4]], find the eigenvalues and eigenvectors. Then explain how these concepts apply to real-world engineering problems.
💡 Hint: Follow the steps through the characteristic equation.
Calculate the eigenvalues for a 3x3 symmetric matrix and justify their properties.
💡 Hint: Consider properties of symmetry!
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