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Math Help - Linear Independence

  1. #1
    Ife
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    Linear Independence

    Determine if the following vectors are linearly independent.

    \begin{bmatrix} 5 \\ 0 \\ 0 \end{bmatrix}<br />
, \begin{bmatrix} 7 \\ 2 \\ -6 \end{bmatrix}<br />
, \begin{bmatrix} 9 \\ 4 \\ -8 \end{bmatrix}<br />


    When i row reduced the augmented matrix, i was getting no solution. Am I correct? And in a situation like that, how do you answer the question? What's the best way to phrase a response?? Or is there something that you do in situations of such?

    Would be grateful for whatever help. Thanks a lot.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Ife View Post
    Determine if the following vectors are linearly independent.

    \begin{bmatrix} 5 \\ 0 \\ 0 \end{bmatrix}<br />
, \begin{bmatrix} 7 \\ 2 \\ -6 \end{bmatrix}<br />
, \begin{bmatrix} 9 \\ 4 \\ -8 \end{bmatrix}<br />


    When i row reduced the augmented matrix, i was getting no solution. Am I correct? And in a situation like that, how do you answer the question? What's the best way to phrase a response?? Or is there something that you do in situations of such?

    Would be grateful for whatever help. Thanks a lot.
    Did you try taking the determinant? If \begin{vmatrix}5 & 7 & 9\\0 & 2 & 4\\ 0 & -6 & -8\end{vmatrix}=0, its linearly dependent. Otherwise, its independent.

    If you row reduce the augmented matrix, you shouldn't get no solution...
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