Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 3 / 7F / a

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- Solution a

Solution

True. Both vector subspaces contain zero, and if

u, v \in U \cap W

, every linear combination

αu + β v

belongs to each of

U

and

W

. Thus it belongs to their intersection. This proves the intersection of vector subspaces is a vector subspace.

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