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Homework Help: Linear dependent

  1. Nov 21, 2006 #1

    lo2

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    I have these 3 vectors. And I have to prove that they are dependent.

    a=(-1,7,-4)

    b=(3,5,-6)

    a=(15,-1,-12)

    I have tried to make 3 equtations with 3 unknows and the solve it. But I just get that the constants should be 0, what they should not be in order to prove they are dependent?
     
  2. jcsd
  3. Nov 21, 2006 #2
    So [tex] A = \begin{bmatrix}
    -1&7&4 \\

    \end{bmatrix}[/tex]

    So [tex] B = \begin{bmatrix}
    3&5&-6 \\

    \end{bmatrix}[/tex]

    So [tex] C = \begin{bmatrix}
    15&-1&-12 \\

    \end{bmatrix}[/tex]

    For the vectors to be linearly dependent, [tex] \left| \begin{array} {ccc} -1 & 7 & 4 \\ 3 & 5& -6 \\ 15 & -1 & -12 \\ \end{array} \right|= 0[/tex]
     
    Last edited: Nov 21, 2006
  4. Nov 21, 2006 #3

    Hootenanny

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    Staff Emeritus
    Science Advisor
    Gold Member

    Alternatively, if you don't like evaluating determinants you could try row reduction to the echelon form (obtaining a final row of zeros would indicate LD).
     
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