Unformatted text preview: L1, where L is from Exercise 1 . iii) Generalize the result in the following way: Show that if ( Ta ) n = 0 for some scalar a and operator T : W→ W , then Tb is invertible (for a scalar b ) if and only if a 6 = b . [Hint: consider S = ( ba )1 ( Ta ).] 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 won’t 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
 guiletary
 Linear Algebra, Algebra, Vector Space, Linear map, leftshift linear operator, Toronto Fall term

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