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Math Help - Prove linearly independent

  1. #16
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    Quote Originally Posted by Raoh View Post
    yes i am.
    I think he proving by contradiction, suppose L.D then get L.I
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  2. #17
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    Quote Originally Posted by 450081592 View Post
    I think he proving by contradiction, suppose L.D then get L.I
    he didn't find any contradiction,besides the proof itself needs to be explained.
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  3. #18
    MHF Contributor Bruno J.'s Avatar
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    One way to prove that P \longrightarrow Q is to show that - Q \longrightarrow -P, which is what I did. If u,v,w are linearly dependent then S must be linearly dependent. Thus if S is linearly independent we must necessarily have that u,v,w are also linearly independent.

    The proof is given. Which part don't you understand?
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  4. #19
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    Quote Originally Posted by Raoh View Post
    he didn't find any contradiction,besides the proof itself needs to be explained.
    He did find a contradiction- that the set of vectors S =\{au+bv+cw,\ du+ev+fw,\ gu+hv+iw\} was linearly dependent when the hypothesis is that it was independent.

    And I thought his proof was very clear.
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  5. #20
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    if u,v and w were dependent, \text{dim}_{\mathbb{R}}Span(u,v,w)\leq 2,therefore u,v and w will be in Span(u,v,w) with a dimension less than 2,hence they can't be independent.
    is that what you're trying to say
    P.S: i like your proof i just can't see through it.
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