(a) To Prove:
Given:
Concept used:
Cayley-Hamilton theorem:
Proof:
For matrix
So we get the eigenvalues of
Now we will compute
So we get
Hence Cayley Hamilton theorem is verified.
Conclusion:
Cayley-Hamilton theorem is verified.
(b) To Prove:
Test the Cayley Hamilton Theorem on Fibonacci's
Given:
Concept used:
Fibonaccis' theorem:
Calculation:
The matrix
The matrix
Now using matrices
So, we get
Hence Cayley Hamilton theorem is verified.
Conclusion:
Cayley-Hamilton theorem is verified.
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Introduction to Linear Algebra, Fifth Edition
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