Ans-265FE-S2001 - .5 3 4 t5e3 5 1 4 te 5 3 4 t3e2 =)t(x)c 5 5 3 3 2 3 2 3 2 1.5 3 4 t5e3c 5 1 4 te2c 5 3 4 t3e1c =)t(x)b 5 5 3 3 2 3 2 3 2 5 1.81 1

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MA 265 FINAL EXAM Spring 2001 ANSWERS 1. (a) 3. (b) 2 6 6 6 4 3 ¡ 2 1 0 0 3 7 7 7 5 , 2 6 6 6 4 ¡ 5 3 0 0 1 3 7 7 7 5 . (c) A 1 , A 2 , A 4 . (d) A 1 , A 2 , A 3 . 2. a =3. 3. · 12 0 03 ¡ 2 ¸ . 4. a = ¡ 8. 5. x ¡ 3 5 = y +1 ¡ 4 = z . 6. 2 4 010 2 ¡ 2 ¡ 1 ¡ 11 1 3 5 . 7. ¡ 5. 8. · 7 ¡ 4 52 ¸ . 9. 3. 10. 2 4 3 0 ¡ 3 3 5 . 11. 2 6 6 6 6 6 4 1 p 2 1 p 2 0 0 3 7 7 7 7 7 5 , 2 6 6 6 6 6 4 1 p 2 ¡ 1 p 2 0 0 3 7 7 7 7 7 5 , 2 6 4 0 0 0 ¡ 1 3 7 5 . 12. (a) True. (b) False. (c) False. (d) True. (e) True. 13. (a) Yes. (b) No. (c) No. (d) Yes. (e) Yes. 14. (a) Independent. (b) Dependent. (c) Dependent. (d) not span. (e) span. 15. (a) ¸ 1 = ¡ 1, P 1 = · 2 1 ¸ . ¸ 2 =1, P 2 = · 7 4 ¸ . (b) P = · 27 14 ¸ ,¤= · ¡ 10 01 ¸ . 16. y =2. 17. (a) ¸ 1 =3+5 i , P 1 = · i 1 ¸ . ¸ 2 =3 ¡ 5 i , P 2 = · ¡ i 1 ¸ . (b) x ( t )= c 1 e 3 t · ¡ sin 5 t cos 5 t ¸ + c 2 e 3 t · cos 5 t sin 5 t ¸ . 18. (a) (a) ¸ 1 = ¡ 3, P 1 = 2 4 3 ¡
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