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 pnorm 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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 '09
 Math, Vectors, Conic section, orthogonal projector

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