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Unformatted text preview: Linear Algebra MAS4105 6137 PrereqA Prof. JLF King 24Aug2011 A1: On your own sheets of paper, please write ( doublespaced ) a proof of the following, in complete English sentences. Do not restate the problem. Let L ( n ) := [5 [2 n ] ] 1. By induction on k , prove that k N : L ( k ) is a multiple of 3. A2: Show no work. NOTE : The inversefnc of g , often written as g 1 , is different from the reciprocal fnc 1 /g . E.g, suppose g is invertible with g ( 2) = 3 and g (3) = 8: Then g 1 (3) = 2, yet [1 /g ](3) def === 1 /g (3) = 1 / 8. Please write DNE in a blank if the described object does not exist or if the indicated operation cannot be performed. a 2 27 3 = ........... . log 8 (4)= ........... . b Line y = [ M x ] + B owns points (3 , 1) and ( 3 , 17). Hence M = ............... and B = ............... . c Quadratic 15 x 2 + 23 x + 6 = [ Ax ] [ Bx ], for numbers A = ........
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This note was uploaded on 01/26/2012 for the course MAS 4105 taught by Professor Rudyak during the Fall '09 term at University of Florida.
 Fall '09
 RUDYAK

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