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**Unformatted text preview: **Mathematic 104, Fall 2010: Assignment #5 Due: Wednesday, November 10th Instructions: Please ensure that your answers are legible. Also make sure that all steps are shown even for problems consisting of a numerical answer. Bonus problems cover advanced material and, while good practice, are not required and will not be graded. Problem #1. Let A R 2 2 be the following matrix A = 1 2- 1 Denote by S p = { u R 2 : || u || p = 1 } the set of vectors of length 1 in the p-norm and let AS p = { Au R 2 : u S p } be the image under A of S p . Here 1 p . a) Determine || A || 1 and find vectors u S 1 and v = Au AS 1 so that || v || 1 = || Au || 1 = || A || 1 . Sketch S 1 and AS 1 and indicate the vectors u and v on the sketch. b) Determine || A || and find vectors u S and v = Au AS so that || v || = || Au || = || A || . Sketch S and AS and indicate the vectors u and v on the sketch....

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