# Ans4 - Answers to Practice Problem Set#4 1(a √ 40(b vectoru 1 =(3 6 5 6 1 6 1 6 T vectoru 2 = − 1 2 1 2 − 1 2 − 1 2 T(c vectorw = 3 vectoru

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Unformatted text preview: Answers to Practice Problem Set #4 1. (a) √ 40 (b) vectoru 1 = (3 / 6 , 5 / 6 , 1 / 6 , 1 / 6) T , vectoru 2 = ( − 1 / 2 , 1 / 2 , − 1 / 2 , − 1 / 2) T (c) vectorw = 3 vectoru 1 + 3 vectoru 2 (d) ˆ y = (1 , − 1 , 1 , 1) T , vector z = (0 , , − 1 , 1) T 2. (a) x 1 + 2 x 2 + 3 x 3 + 4 x 4 = 0, 5 x 1 + 6 x 2 + 7 x 3 + 8 x 4 = 0 (b) vectorx i · vectorx j = 0 for all 1 ≤ i, j ≤ k such that i negationslash = j (c) Column space of A (d) { (1 , , 0) T , (0 , 1 , 0) T , (0 , , 1) T } 3. ˆ x = (1 , 1 / 7) T , error= √ 238 / 7 4. (a) 0, 4 (b) { ( − 2 , 1) T , (2 , 1) T } (c) vectorx ( t ) = ( − 2 , 1) T + 2 e 4 t (2 , 1) T 5. (a) 2 + i , 2 − i (b) { ( − 1 + i, 1) T , ( − 1 − i, 1) T } (c) 1, 5, 8, 4 (d) (1 , , , 0) T 6. (a) 5 (b) i. 3 ii. 6 iii. Infinitely many iv. Can’t tell 7. (a) 1 3 0 0 0 1 0 0 0 (b) { (1 , 3 , 0) T , (0 , , 1) T } (c) { (1 , 1 , 2) T , (6 , 7 , 8) T } (d) { ( − 3 , 1 , 0) T } 8. (a) i. 2 ii. 12 iii. 8 (b) { c 1 vectorx 1 +...
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## This note was uploaded on 12/27/2011 for the course MAS 3114 taught by Professor Olson during the Fall '08 term at University of Florida.

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Ans4 - Answers to Practice Problem Set#4 1(a √ 40(b vectoru 1 =(3 6 5 6 1 6 1 6 T vectoru 2 = − 1 2 1 2 − 1 2 − 1 2 T(c vectorw = 3 vectoru

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