hw11 - p (b Show that tr A is equal to the sum of the...

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Math 110—Linear Algebra Fall 2009, Haiman Problem Set 11 Due Monday, Nov. 16, at the beginning of lecture, along with Problem Set 10. 1. Let A be a n × n matrix whose characteristic polynomial p ( λ ) = det( A - λI ) splits as a product of linear factors. (a) Show that det( A ) is equal to the product of the eigenvalues of A , each repeated as many times as its multiplicity as a root of
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Unformatted text preview: p ( λ ). (b) Show that tr( A ) is equal to the sum of the eigenvalues of A , each repeated as many times as its multiplicity as a root of p ( λ ). [Hint: consider the coefficient of λ n-1 in p ( λ ).] 2. Section 5.2, Exercise 14(c). 3. Find formulas for A n and e At , where A = ± 1 2 4 3 ² ....
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