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Unformatted text preview: Math 3330 SOLUTIONS FOR PRACTICE FINAL EXAM 1. Augmented matrix: A = 1 2 1 2 2 3 1 1 4 1 1 3 . Gaussian elimination: 1 2 1 2 2 3 1 1 4 1 1 3 R 2 → R 2 2 R 1 1 2 1 2 1 1 3 1 1 3 R 3 → R 3 R 2 1 2 1 2 1 1 3 . Pivot variables: x and y , nonpivot variables: z and w . Let z = s , w = t . Then y = s + 3 t , x = 2 + 2 s 5 t . In paramtertic form, x y w z = 2 + s 2 1 1 + t  5 3 1 . The spanning vectors are 2 1 1 ,  5 3 1 and the translation vector, 2 . 2. W contains the 0 function. Let f and g be two functions from W . ( f + g )(2) = f (2) + g (2) = 0 + 0 = 0, thus f + g lies in W as well. If f is a function from W and c any constant, then ( cf )(2) = cf (2) = 0, thus cf lies in W as well....
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This note was uploaded on 02/17/2011 for the course MATH 3330 taught by Professor Staff during the Spring '08 term at UT Arlington.
 Spring '08
 Staff
 Linear Algebra, Algebra, Gaussian Elimination

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