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Vector Spaces, Subspaces and Dimension

V3(R) represents the set of vectors in 3D space. What kind of geometrical objects are represented by the various subspaces of V3(R)?

i.e A 1D subspace S with basis { (0, 1, 0)Transpose} 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.

You need only consider subspaces of dimension less than 3.

Solution Preview

A line passing through origin represents the 1-dimensional subspace of V3.
Here are some examples:
S1 = <(1,0,0)^T> is the x-axis
S2 = <(0,1,0)^T> is the y-axis
S3 = <(0,0,1)^T> is the z-axis
Now we ...

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