summer2004-final - Name MAS 3114 Computational Linear...

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Unformatted text preview: Name: MAS 3114 Computational Linear Algebra Summer A 2004 FINAL EXAM Instructions: • There are 11 questions, including an 18 point bonus problem. • There 170 points available. Full marks (100%) will be given for 150 points. • Write on ONE side of your paper. • Show all necessary working and reasoning to receive full credit. • Your work needs to be written in a proper and coherent fashion. • When giving proofs your reasoning should be clear. • Only scientific calculators are allowed. • Questions with may be answered on the exam paper. 1 1. [4 + 10 + 4 = 18 points] (a) (i) Let v 1 , v 2 ,..., v p be vectors in R n . Define the set denoted by Span { v 1 , v 2 ,..., v p } . (b) Let v 1 = 1 1- 1 , v 2 = 1- 1 , v 3 = 2- 1 . Let W = Span { v 1 , v 2 , v 3 } . (i) Show that x = a b c is in the subspace W , if and only if a + b + 2 c = 0. (ii) Find dim W giving reason. 2. [4 points] Complete the following definition : A set { v 1 , v 2 ,..., v p } in R n is said to be linearly independent if the vector equation has . 3. [8 points] Let v 1 = 1- 1- 1 , v 2 = - 1 2 2- 1 , v 2 = - 1...
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This note was uploaded on 12/27/2011 for the course MAS 3114 taught by Professor Olson during the Fall '08 term at University of Florida.

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summer2004-final - Name MAS 3114 Computational Linear...

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