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Linear Algebra

Exercise 1.6.34

Answers

1.: Let $β$ be the basis of $V$ and $α$ be the basis of $W_{1}$ . By Replacement Theorem we can extend $α$ to be a basis $α^{'}$ of $V$ such that $α \subset α^{'}$ . By the previous exercise and let $W_{2} =$ span $(α^{'} ∖ α)$ , we have $V = W_{1} \oplus W_{2}$ .
2.: We may set $W_{2}$ to be the $y$ -axis and $W_{2}^{'}$ to be ${t (1, 1) : t \in ℝ}$ .

jephianlin

2011-06-27 00:00

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