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Math Help - linear independence

  1. #1
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    linear independence

    Show that the following is linearly independent or express one of the vectors in the set as a linear combination of the others.

    {[2,1],[3,2],[1,2]}

    Ok, this is what I had:
    C_1*V_1 + C_2*V_2+.....+C_N*V_N = 0

    2C_1+3C_2+C_3=0
    C_1+2C_2+2C_3=0
    But the thing is that I can't figure out how to use the method of elimination here. Help?
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  2. #2
    A Plied Mathematician
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    Try multiplying the second row by -2, adding the first row to it, and storing the result in the second row.
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  3. #3
    MHF Contributor
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    I like to use a matrix. You can use the rref to find the linear combination if there is one.

    \displaystyle<br />
\begin{bmatrix}2&3&1\\1&2&2\end{bmatrix}\Rightarro  w \mbox{rref}=\begin{bmatrix}1&0&-4\\0&1&3\end{bmatrix}

    V_3=-4V_1+3V_2

    Another thing to note is you have 3 vectors in \mathbb{R}^2.
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