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True/False Question: If sppan{u,v}=W where u not equal to v. Then dim(W)=2. Answer: False Reasoning let u=1, v=2...

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Advance Math

True/False Question: If sppan{u,v}=W where u not equal to v.Then dim(W)=2.

Answer: False

Reasoning let u=1, v=2 then span(1,2}=R but dim(R)=1 not 2.

I know the answer is false. please tell me whether my reasoningis correct.

Answer & Explanation Solved by verified expert
3.7 Ratings (457 Votes)
your reasoning is wrong how spanuv means set of all linear combinations of u and v And spanuvW then dimensions of W can b 1 or 2 depending on u and v and u can not say dimW 2 thats false now two cases    See Answer
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