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Unformatted text preview: L-1, where L is from Exercise 1 . iii) Generalize the result in the following way: Show that if ( T-a ) n = 0 for some scalar a and operator T : W- W , then T-b is invertible (for a scalar b ) if and only if a 6 = b . [Hint: consider S = ( b-a )-1 ( T-a ).] 1 Reading suggestion: Read the rest of Axler Chapter 3 very carefully, and familiarize yourself with Chapter 4- it contains some basic results about polynomials in one variable. We wont be going through it in great detail, but you should be comfortable working with polynomials. 2 I encourage you to work together on the ideas but the solutions must be individual. 3 Neatness counts, and so does being concise. 4 Please submit the questions in the correct order. 1...
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- Fall '10