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Exercise 2.7.7

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Let $W$ and $V$ be the two subspaces generated by the two sets ${x, y}$ and ${\frac{1}{2} (x + y), \frac{1}{2 i} (x - y)}$ separately. We know that $W \supset V$ since $\frac{1}{2} (x + y)$ and $\frac{1}{2 i} (x - y)$ are elements in $W$ . And it is also true that $W \subset V$ since

x = \frac{1}{2} (x + y) + \frac{i}{2 i} (x - y)

and

y = \frac{1}{2} (x + y) - \frac{i}{2 i} (x - y)

are elements in $V$ .

jephianlin

2011-06-27 00:00

Exercise 2.7.7

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