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Unformatted text preview: 2 , 5] , and a 3 = [5 / 2 , 3 , 5] . Are these vectors linearly independent? Do they span R 3 ? 1 Exercise 4 Find the hyperplane H in R 4 which contains the four points e 1 , e 1 + 2 e 2 , e 2 + 3 e 3 , e 3 + 4 e 4 where { e 1 ,e 2 ,e 3 ,e 4 } is the canonical basis for R 4 . Exercise 5 Find the hyperplane in R 4 containig the four points , e 1 + e 2 , e 1e 2 +2 e 3 , 3 e 4e 2 . Find also the value of t for which t ( e 1e 2 )+(1t ) e 4 is in the hyperplane. Exercise 6 Let l denote the line in R 4 through e 1e 3 ande 1 + e 2 + 2 e 4 . Find the hyperplane H through e 1e 3 to which l is perpendicular. Exercise 7 Find a linear programming model for the Wyndor Glass Co. problem. Explain what you do. Draw the feasible set for this problem as well. 2...
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 Spring '10
 GROSSMAN
 Linear Algebra, Linear Programming, EMC E4

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