21.12.1 - Statement
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Practice Questions
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What is the Cayley-Hamilton theorem?
💡 Hint: Think about matrices and their equations.
Can a non-singular matrix be inverted?
💡 Hint: Recall the properties of determinants.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Cayley-Hamilton theorem state?
💡 Hint: Think about any distinctions between types of matrices.
True or False: All matrices satisfy the Cayley-Hamilton theorem.
💡 Hint: Consider the definition of square matrices.
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Challenge Problems
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Given the matrix A = [[4, 1], [2, 3]], calculate its characteristic polynomial, apply the Cayley-Hamilton theorem, and find A^{-1} with the theorem's help.
💡 Hint: Utilize the determinant and characteristics from previous examples.
Using the Cayley-Hamilton theorem, express A^4 in terms of A^3 and A^2 for the matrix A = [[1, 2], [0, 1]].
💡 Hint: Consider the pattern formed in the powers of A to simplify.
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