hw9s - MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011, Key...

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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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hw9s - MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011, Key...

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