Always use the field F=R of real numbers. Here is a living solutions manual.
6.2 Exercises (p.352) 1(a,b,f,g)
5.4 Exercises (p. 321) 1(a, b, c, d), 5, 17
6.1 Exercises (p. 336) 1(d, e, g, h), 8, 10, 17
5.2 Exercises (p. 256) 11, 12
5.3 Exercises (p. 307) 5, 12 and one more.
5.1 Exercises (p. 256) 1(b,c,e,h,i,j), 2(b,d), 7, 12
5.2 Exercises (p. 279) 1(a,b,c,d), 2(b,d,f), 8
3.2 Exercises (p. 165) 1, 5ab, 7
4.1 Exercises (p. 207) 1, 4ab, 5
2.4 Exercises (p.106) 1, 4, 7
2.5 Exercises (p. 116) 1, 4, 10
3.1 Exercises (p.151) 1, 3
2.2 Exercises (p. 84) 1, 3
2.3 Exercises (p. 96) 1, 3, 13
2.1 Exercies (p.74) 1, 3, 6, 7, 10, 15, 16, 18, 19
Note that 15, 16 are counterexamples to Thm 2.5 for infinite dimension.
1.4 Exercises (p.32) 9, 10, 13, 15
1.6 Exercises (p. 53) 1, 4, 11, 20, 24, 26
1.3 Exercises (p.19) 1, 4, 5, 15, 17
1.4 Exercises (p. 32) 1, 2, 4
1.5 Exercises (p. 40): 1, 10, 12, 14
1.1 Exercises (p.5) 1a, 2a, 3a, 6, 7
1.2 Exercises (p.12) 8,9