# Q e 1 42 q e 2 36 c x 1 1 10 x 1 3 40 x 2 x 1 0 17 x

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Q E 1 = 42 , Q E 2 = 36 c. x 1 = − 1 10 x 1 + 3 40 x 2 , x 1 (0) = − 17 , x 2 = 1 10 x 1 1 5 x 2 , x 2 (0) = − 21 20. a. Q 1 = 3 q 1 1 15 Q 1 + 1 100 Q 2 , Q 1 (0) = Q 0 1 , Q 2 = q 2 + 1 30 Q 1 3 100 Q 2 , Q 2 (0) = Q 0 2 b. Q E 1 = 6(9 q 1 + q 2 ) , Q E 2 = 20(3 q 1 + 2 q 2 ) c. No d. 10 9 Q E 2 Q E 1 20 3 Section 7.2, page 293 1. a. 6 6 3 5 9 2 2 3 8 b. 15 6 12 7 18 1 26 3 5 c. 6 12 3 4 3 7 9 12 0 d. 8 9 11 14 12 5 5 8 5 2. a. ( 1 i 7 + 2 i 1 + 2 i 2 + 3 i ) b. ( 3 + 4 i 6 i 11 + 6 i 6 5 i ) c. ( 3 + 5 i 7 + 5 i 2 + i 7 + 2 i ) d. ( 8 + 7 i 4 4 i 6 4 i 4 ) 3. a. 2 1 2 1 0 1 2 3 1 b. 1 3 2 2 1 1 3 1 0 c, d. 1 4 0 3 1 0 5 4 1

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Boyce 9131 BMAnswersToProblems 2 March 11, 2017 15:55 588 588 Answers to Problems 4. a. ( 3 2 i 2 i 1 + i 2 + 3 i ) b. ( 3 + 2 i 1 i 2 + i 2 3 i ) c. ( 3 + 2 i 2 + i 1 i 2 3 i ) 5. a. 7 11 3 11 20 17 4 3 12 b. 5 0 1 2 7 4 1 1 4 c. 6 8 11 9 15 6 5 1 5 7. a. 4 i b. 12 8 i c. 2 + 2 i d. 16 8. 3 11 4 11 2 11 1 11 9. 1 6 1 12 1 2 1 4 10. 1 3 2 3 3 1 2 1 0 11. Singular 12. 1 2 1 4 1 8 0 1 2 1 4 0 0 1 2 13. Singular 14. 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 16. a. 7 e t 5 e t 10 e 2 t e t 7 e t 2 e 2 t 8 e t 0 e 2 t b. 2 e 2 t 2 + 3 e 3 t 1 + 4 e 2 t e t 3 e 3 t + 2 e t e 4 t 4 e 2 t 1 3 e 3 t 2 + 2 e 2 t + e t 6 e 3 t + e t + e 4 t 2 e 2 t 3 + 6 e 3 t 1 + 6 e 2 t 2 e t 3 e 3 t + 3 e t 2 e 4 t c. e t 2 e t 2 e 2 t 2 e t e t 2 e 2 t e t 3 e t 4 e 2 t d. ( e 1) 1 2 e 1 1 2 ( e + 1) 2 e 1 1 2 ( e + 1) 1 3 e 1 e + 1 Section 7.3, page 303 1. x 1 = − 1 3 , x 2 = 7 3 , x 3 = − 1 3 2. No solution 3. x 1 = − c, x 2 = c + 1 , x 3 = c , where c is arbitrary 4. x 1 = c, x 2 = − c, x 3 = − c, where c is arbitrary 5. x 1 = 0 , x 2 = 0 , x 3 = 0 6. Linearly independent 7. x (1) 5 x (2) + 2 x (3) = 0 8. Linearly independent 9. x (1) + x (2) x (4) = 0 11. 3 x (1) ( t ) 6 x (2) ( t ) + x (3) ( t ) = 0 12. Linearly independent 14. 𝜆 1 = 2 , x (1) = ( 1 3 ) ; 𝜆 2 = 4 , x (2) = ( 1 1 ) 15. 𝜆 1 = 1 + 2 i, x (1) = ( 1 1 i ) ; 𝜆 2 = 1 2 i, x (2) = ( 1 1 + i ) 16. 𝜆 1 = − 3 , x (1) = ( 1 1 ) ; 𝜆 2 = − 1 , x (2) = ( 1 1 ) 17. 𝜆 1 = 2 , x (1) = (√ 3 1 ) ; 𝜆 2 = − 2 , x (2) = ( 1 3 ) 18.
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• Spring '16
• Anhaouy
• Districts of Vienna, Boyce, e2t, 3y, = min, + c2 sin x

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