Unformatted text preview: which is linearly dependant. ∅ ⊂ { } is linearly independant. 1.6.22 The condition is that W 1 ⊂ W 2 , thus we must prove that ”dim( W 1 ∩ W 2 ) = dim( W 1 ) if and only if W 1 ⊂ W 2 .” Let dim( W 1 ∩ W 2 ) = dim( W 1 ). As W 1 ∩ W 2 ⊂ W 1 , we see that our assumption gives that W 1 ∩ W 2 = W 1 . Thus W 1 = W 1 ∩ W 2 ⊂ W 2 . Conversely let W 1 ⊂ W 2 . Thus W 1 ∩ W 2 = W 1 giving that dim( W 1 ∩ W 2 ) = dim( W 1 )....
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 Spring '10
 FUCKHEAD
 WI

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