This problem establishes a special case of the Cayley-Hamilton theorem.
a) Prove that if
b) Suppose that if
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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two distinct real eigenvalues, one real eigenvalue, and no real eigenvalues.arrow_forwarda Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving that if A is an nn symmetric matrix with positive eigenvalues, then there exists a symmetric matrix B such that B2=A.arrow_forward
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