Prove the statement: If u, v, and w are linearly independent, then u+v, v, and w are also linearly independent.
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Originally Posted by ssl000 Prove the statement: If u, v, and w are linearly independent, then u+v, v, and w are also linearly independent. Given: only when are equal to zero. Now re-write as ....
Last edited by mr fantastic; Dec 21st 2008 at 11:01 PM. Reason: Misread the question
Originally Posted by mr fantastic Given: where not all of the are equal to zero. This can be re-written as where .... Wouldn't that prove that its linearly dependent, since ?
Originally Posted by ssl000 Wouldn't that prove that its linearly dependent, since ? Sorry I misread the question. I've edited my reply accordingly.
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