Exercise 7.4.9

Answers

Since the disjoint union of $β_{i}$ ’s is a basis, each $β_{i}$ is independent and forms a basis of $span (β_{i})$ . Now denote

W_{i} = span (γ_{i}) = span (β_{i}) .

Thus $V = ⊕_{i} W_{i}$ by Theorem 5.10. And the set $γ = ∪_{i} γ_{i}$ is a basis by Exercise 1.6.33.

jephianlin

2011-06-27 00:00