Thread: dimension
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Old January 11th, 2009, 11:12 PM
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Quote:
Originally Posted by Kat-M View Post
Let V be a finite dimensional vector space. Show that if W1,....,Wn are subspaces of V such that none of these subspaces are qeual to V, then Union of all these subspaces does not equal V.
The union of two subpaces is a subspace if and only one is contained in another.
Thus if W_1\cup W_2 is a subspace thus W_1\subseteq W_2 and W_2\subseteq W_1.
And so \dim (W_1\cap W_2) = \max \{ \dim (W_1),\dim (W_2) \} < \dim (V).
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