Section 4.1

1. $\sqrt{51}$ $\sqrt{51}$ , $(5, 8, - 11)$ $(5, 8, - 11)$ , $(2, 23, 0)$ $(2, 23, 0)$
2. 9, $(1, 4, - 1)$ $(1, 4, - 1)$ , $(- 15, - 16, 26)$ $(- 15, - 16, 26)$
3. $3 \sqrt{21}, 9 i - 3 j + 3 k, - 14 i - 21 j + 43 k$ $3 \sqrt{21}, 9 i - 3 j + 3 k, - 14 i - 21 j + 43 k$
4. $\sqrt{17}, 4 i - j - 3 k, 6 i - 7 j + 12 k$ $\sqrt{17}, 4 i - j - 3 k, 6 i - 7 j + 12 k$
5. Linearly dependent
6. Linearly dependent
7. Linearly dependent
8. Linearly dependent
9. $w = 3 u + 2 v$ $w = 3 u + 2 v$
10. $w = 2 u - 3 v$ $w = 2 u - 3 v$
11. $w = u - 2 v$ $w = u - 2 v$
12. $w = 3 u + 5 v$ $w = 3 u + 5 v$
13. $w = 2 u - 3 v$ $w = 2 u - 3 v$
14. $w = 7 u + 5 v$ $w = 7 u + 5 v$
15. Linearly dependent
16. Linearly dependent
17. Linearly dependent
18. Linearly dependent
19. Linearly dependent; $a = 3, b = 2, c = 1$ $a = 3, b = 2, c = 1$
20. Linearly dependent; $a = - 2, b = 3, c = 1$ $a = - 2, b = 3, c = 1$
21. Linearly dependent; $a = 11, b = 4, c = - 1$ $a = 11, b = 4, c = - 1$
22. Linearly dependent
23. Linearly dependent
24. Linearly dependent
25. $t = 2 u - v + 3 w$ $t = 2 u - v + 3 w$
26. $t = u + 5 v - w$ $t = u + 5 v - w$
27. $t = 2 u + 6 v + w$ $t = 2 u + 6 v + w$
28. $t = u + v + w$ $t = u + v + w$

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Table of Contents for Section 4.1