Differential Equations and Linear Algebra, 4th Edition

Section 4.2

1. 1. W is a subspace of ${\mathbf{R}}^3$.

2. 2. W is a subspace of ${\mathbf{R}}^3$.

3. 3. W is not a subspace of ${\mathbf{R}}^3$.

4. 4. W is not a subspace of ${\mathbf{R}}^3$.

5. 5. W is a subspace of ${\mathbf{R}}^4$.

6. 6. W is a subspace of ${\mathbf{R}}^4$.

7. 7. W is not a subspace of ${\mathbf{R}}^2$.

8. 8. W is a subspace of ${\mathbf{R}}^2$.

9. 9. W is not a subspace of ${\mathbf{R}}^2$.

10. 10. W is not a subspace of ${\mathbf{R}}^2$.

11. 11. W is a subspace of ${\mathbf{R}}^4$.

12. 12. W is not a subspace of ${\mathbf{R}}^4$.

13. 13. W is not a subspace of ${\mathbf{R}}^4$.

14. 14. W is not a subspace of ${\mathbf{R}}^4$.

15. 15. $\mathbf{u}=\left(-1,\text{ 0,}\text{1,}\text{0}\right)$ and $\mathbf{v}=\left(-4,-2,0,1\right)$

16. 16. $\mathbf{u}=\left(-1,-1,0,1\right)$ and $\mathbf{v}=\left(-5,-3,0,1\right)$

17. 17. $\mathbf{u}=\left(1,-3,-2,0\right)$ and $\mathbf{v}=\left(-2,1,0,1\right)$

18. 18. $\mathbf{u}=\left(2,-1,-2,1,0\right)$ and $\mathbf{v}=\left(3,-4,5,0,1\right)$

19. 19. $\mathbf{u}=\left(1,2,-1,0\right)$

20. 20. $\mathbf{u}=\left(-5,3,-2,1\right)$

21. 21. $\mathbf{u}=(-3,2,-4,1)$

22. 22. $\mathbf{u}=(-6,4,-3,1)$