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Unformatted text preview: MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011, Key to HW#9 Note : All the problems below are related to Theorem 3.16 on Page 191. So please read the understand Theorem 3.16 before doing the following home work. 1. Problem 5 Page 196. Solution . By Theorem 3.16, the third column of A is 2 1 1 3  5  1 1 = 2 3 1 . The fifth column of A is 2 1 1 3  3  1 1 + 6 1 2 = 4 7 9 . Hence A = 1 2 1 4 1 1 3 2 7 3 1 1 9 . 2. Problem 7 on Page 197. Solution . 2 1 8 1 3 3 4 12 37 5 1 2 4 17 8 → 1 2 4 17 8 5 35 19 2 14 19 → 1 0 4 31 27 0 1 7 19 / 2 0 0 70 133 / 2 → 1 0 4 0 * 0 1 * 0 0 1 133 / 140 So { u 1 , u 2 , u 4 } is a basis for R 3 . 1 3. Problem 9 on Page 197. Solution . 1 2 1 1 1 2 1 2 2 1 3 9 4 1 → 1 3 9 4 1 0 1 2 1 1 0 0 0 3 6 So { u 1 ,u 2 ,u 4 } is a basis for W....
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This note was uploaded on 02/21/2012 for the course MATH 4377 taught by Professor Staff during the Summer '08 term at University of Houston.
 Summer '08
 Staff
 Linear Algebra, Algebra

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