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Math Help - Vector True or False Help!

  1. #1
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    Vector True or False Help!

    If v1,...v4 are in R4 and v3 is not a linear combination of v1, v2, v3, v4 then {v1, v2, v3, v4} is linearly independent.

    I'm pretty sure this statement is false but I don't know how to prove it. Can someone please help me?
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  2. #2
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    Quote Originally Posted by zerobladex View Post
    If v1,...v4 are in R4 and v3 is not a linear combination of v1, v2, v3, v4 then {v1, v2, v3, v4} is linearly independent.

    I'm pretty sure this statement is false but I don't know how to prove it. Can someone please help me?
    Hi - Are you sure you got the question correct please? Because v3 is definately a linear combination of v1, v2, v3, v4
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  3. #3
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    Quote Originally Posted by zerobladex View Post
    If v1,...v4 are in R4 and v3 is not a linear combination of v1, v2, v3, v4 then {v1, v2, v3, v4} is linearly independent.
    I'm pretty sure this statement is false but I don't know how to prove it. Can someone please help me?
    Reread that statment.
    Do you mean v3 is not a linear combination of v1, v2, v4..."?
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  4. #4
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    Yes, i mean that v3=/= c1v1 + c2v2 + c3v3.
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  5. #5
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    Quote Originally Posted by zerobladex View Post
    Yes, i mean that v3=/= c1v1 + c2v2 + c3v3.


    The claim's false: take v_1 = (1,0,0,0), v_2 = (0,1,0,0), v_3 = (0,0,1,0),
    v_4 = (1,1,0,0) (or v_4 = v_1, or v_4 = v_2, or v_4 = v_3, etc.).

    Then v_3 is not a l.c. of v_1, v_2, but v_4 IS and thus the whole set
    {v_1,v_2,v_3,v_4} is l.d.

    Tonio
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