ans3 - Answers to Practice Problem Set 3 1(b D = −1 2 i 0...

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Unformatted text preview: Answers to Practice Problem Set 3 1. (b) D = −1 + 2 i 0 0 −1 − 2 i (c) a = −1, b = 2 2. (a) µ0 = 3, µ1 = 5, µ2 = 5.2, x1 = 1/3 7/15 , x2 = 1 1 (b) µ0 = −2, µ1 = −2.75, µ2 = −2.6818, ν0 = −.5, ν1 = −.364, 1 1 ν2 = −.373, x1 = , x2 = −.75 −.682 3. (a) vk = (.5)k .2 .8 + 2k .8 −. 8 (b) −1 4. P = −2 −1 20 65 66 ,D= , A5 = 11 0 −1 −33 −34 5. λ = 2 + i, 2 − i, −1 + i 1 , −1 − i 1 6. (a) 1 (b) No (c) 3 (d) Can’t tell (1 or 2) 7. (a) (b) Yes, if Ax = λx then A(cx) = cAx = cλx = λ(cx). 10 then e1 and e2 are eigenvectors for A, but 02 e1 + e2 is not. 11 (d) A = , λ1 − = 1. 01 (c) No, if A = 8. (a) 0, 4 (b) {(−2, 1)T , (2, 1)T } (c) x(t) = (−2, 1)T + 2e4t (2, 1)T 9. (a) 2 + i, 2 − i (b) {(−1 + i, 1)T , (−1 − i, 1)T } (c) 1, 5, 8, 4 (d) (1, 0, 0, 0)T 10. (a) xk = (b) .6 .4 .6 .4 + (.5)k .4 −. 4 ...
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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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