Here is a question I have been given:(adsbygoogle = window.adsbygoogle || []).push({});

V3(R) represents the set of vectors in 3-dimensional space. What kind of geometrical objects are represented by the various subspaces of V3(R)? For instance the 1-dimensional subspace S with basis { (0, 1, 0)T } represents the set of vectors parallel to the y-axis, so the set of points with position vectors in S is the y-axis itself. Since any 3-dimensional subspace of V3(R) is V3(R) itself, you need only consider subspaces of dimension less than 3. You should find that the range of different kinds of geometrical object represented by the subspaces of V3(R) is quite restricted.

I do not know what this is asking.

Does it mean looking at planes?

But surely there is more to the question than that?

Has anyone got any clues or tips.

Cheers

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# Vector Spaces Question

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