Differential Equations and Linear Algebra, 4th Edition

Section 6.1

1. 1. ${\lambda }_1=2$: ${\mathbf{v}}_1=(1,1)$; ${\lambda }_2=3$: ${\mathbf{v}}_2=(2,1)$

2. 2. ${\lambda }_1=-1$: ${\mathbf{v}}_1=(1,1)$; ${\lambda }_2=2$: ${\mathbf{v}}_2=(2,1)$

3. 3. ${\lambda }_1=2$: ${\mathbf{v}}_2=(1,1)$; ${\lambda }_2=5$: ${\mathbf{v}}_1=(2,1)$

4. 4. ${\lambda }_1=1$: ${\mathbf{v}}_2=(1,1)$; ${\lambda }_2=2$: ${\mathbf{v}}_1=(3,2)$

5. 5. ${\lambda }_1=1$: ${\mathbf{v}}_2=(1,1)$; ${\lambda }_2=4$: ${\mathbf{v}}_1=(3,2)$

6. 6. ${\lambda }_1=2$: ${\mathbf{v}}_2=(1,1)$; ${\lambda }_2=3$: ${\mathbf{v}}_1=(4,3)$

7. 7. ${\lambda }_1=2$: ${\mathbf{v}}_2=(1,1)$; ${\lambda }_2=4$: ${\mathbf{v}}_1=(4,3)$

8. 8. ${\lambda }_1=-2$: ${\mathbf{v}}_2=(2,3)$; ${\lambda }_2=-1$: ${\mathbf{v}}_1=(3,4)$

9. 9. ${\lambda }_1=3$: ${\mathbf{v}}_1=(2,1)$; ${\lambda }_2=4$: ${\mathbf{v}}_2=(5,2)$

10. 10. ${\lambda }_1=4$: ${\mathbf{v}}_1=(2,1)$; ${\lambda }_2=5$: ${\mathbf{v}}_2=(5,2)$

11. 11. ${\lambda }_1=4$: ${\mathbf{v}}_2=(2,3)$; ${\lambda }_2=5$: ${\mathbf{v}}_1=(5,7)$

12. 12. ${\lambda }_1=3$: ${\mathbf{v}}_2=(3,2)$; ${\lambda }_2=4$: ${\mathbf{v}}_1=(5,3)$

13. 13. ${\lambda }_1=0$: ${\mathbf{v}}_1=(0,-1,2)$; ${\lambda }_2=1$: ${\mathbf{v}}_2=(0,-1,3)$; ${\lambda }_3=2$: ${\mathbf{v}}_3=(1,0,2)$

14. 14. ${\lambda }_1=0$: ${\mathbf{v}}_1=(0,-1,2)$; ${\lambda }_2=2$: ${\mathbf{v}}_2=(0,-1,3)$; ${\lambda }_3=5$: ${\mathbf{v}}_3=(1,0,2)$

15. 15. ${\lambda }_1=0$: ${\mathbf{v}}_1=(1,1,0)$; ${\lambda }_2=1$: ${\mathbf{v}}_2=(2,1,1)$; ${\lambda }_3=2$: ${\mathbf{v}}_3=(1,0,2)$

16. 16. ${\lambda }_1=0$: ${\mathbf{v}}_1=(1,1,1)$; ${\lambda }_2=1$: ${\mathbf{v}}_2=(1,1,0)$; ${\lambda }_3=3$: ${\mathbf{v}}_3=(-1,0,2)$

17. 17. ${\lambda }_1=1$: ${\mathbf{v}}_1=(1,0,1)$; ${\lambda }_2=2$: ${\mathbf{v}}_2=(-1,1,2)$;