# Vector space/Subspaces of K^123/Example

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Let be a field. It is easy to get an overview over the linear subspaces of , as the dimension of a linear subspace equals with , due to fact. For , there is only the null space itself, for there is the null space and itself. For , there is the null space, the whole plane , and the one-dimensional lines through the origin. Every line has the form

with a vector . Two vectors different from define the same line if and only if they are linearly dependent. For , there is the null space, the whole space , the one-dimensional lines through the origin, and the two-dimensional planes through the origin.