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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## 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.

Ask a homework question - tutors are online