Differential Equations and Linear Algebra, 4th Edition

Section 3.1

1. 1. $x=3\text{,}y=2$

2. 2. $x=5\text{,}y=-3$

3. 3. $x=-4\text{,}y=3$

4. 4. $x=5\text{,}y=4$

5. 5. Inconsistent—no solution

6. 6. Inconsistent—no solution

7. 7. $x=-10+4t\text{,}y=t$ (infinitely many solutions)

8. 8. $x=4+2t\text{,}y=t$ (infinitely many solutions)

9. 9. $x=4\text{,}y=-1\text{,}z=3$

10. 10. $x=3\text{,}y=1\text{,}z=-2$

11. 11. $x=1\text{,}y=3\text{,}z=-4$

12. 12. $x=1\text{,}y=3\text{,}z=5$

13. 13. $x=y=z=0$

14. 14. $x=5\text{,}y=3\text{,}z=-4$

15. 15. Inconsistent—no solution

16. 16. Inconsistent—no solution

17. 17. Inconsistent—no solution

18. 18. Inconsistent—no solution

19. 19. $x=8+3t\text{,}y=3+2t\text{,}z=t$ (infinitely many solutions)

20. 20. $x=-5t\text{,}y=5+t\text{,}z=t$ (infinitely many solutions)

21. 21. $x=3-2t\text{,}y=2+3t\text{,}z=t$ (infinitely many solutions)

22. 22. $x=-4t\text{,}y=-5t\text{,}z=t$ (infinitely many solutions)

23. 23. $y(x)=3\cos 2x+4\sin 2x$

24. 24. $y(x)=5\cosh 3x+4\sinh 3x$

25. 25. $y(x)=7e^{5x}+3e^{-5x}$

26. 26. $y(x)=23e^{11x}+21e^{-11x}$

27. 27. $y(x)=23e^{3x}+17e^{-}$