hw1 - ( x,y,z ) on R 3 . 1a. The plane in R 3 consisting of...

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MATH 427LAP HOMEWORK 1 Due Monday, August 30th at 3:00PM Marsden and Tromba, 1.1 2,3,6,8,9,11,14,17,20,22,24,25 Additional Problems 1. Give a parametric description of the following subsets of R 2 or R 3 : 1a. The set of points ( x,y ) in R 2 for which 2 x - y 0 and 2 y - x 0. 1b. The triangle in R 3 whose vertices are (1 , 1 , 1), (1 , 2 , 3), and (1 , 3 , 2). 2. For each of the following parametrically described subsets of R 3 , give a description of them in terms of equations and inequalities on the coordinates
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Unformatted text preview: ( x,y,z ) on R 3 . 1a. The plane in R 3 consisting of all points ( x,y,z ) of the form (1 + t + u, 1 + 2 t + u, 1 + u + 2 t ) for some real numbers t and u . 1b. The set of all points ( x,y,z ) in R 3 of the form (1+ t + u, 1+2 t + u, 1+ u +2 t ) where 0 t 1 and 0 u 1. 1c. The set of all points ( x,y,z ) in R 3 of the form (1 + t + u, 1 + 2 t + u, 1 + u + 2 t ), where 1 t 2 and 1 u 2. 1...
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This note was uploaded on 11/26/2011 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.

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