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Math Help - Linearly Independent

  1. #1
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    Linearly Independent

    I need help on the following problem:

    The vectors v =  \begin{bmatrix} 0\\-4\\-8 \end{bmatrix} , u =  \begin{bmatrix} -4\\8\\28+k \end{bmatrix}, and w =  \begin{bmatrix} 2\\-4\\-14 \end{bmatrix} are linearly independent if and only if  k \neq ?
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  2. #2
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    Quote Originally Posted by MagicS06 View Post
    I need help on the following problem:

    The vectors v =  \begin{bmatrix} 0\\-4\\-8 \end{bmatrix} , u =  \begin{bmatrix} -4\\8\\28+k \end{bmatrix}, and w =  \begin{bmatrix} 2\\-4\\-14 \end{bmatrix} are linearly independent if and only if  k \neq ?
    The vectors are independet if and only if the following matrix has rank=3, so find k that makes rank<3

    \left ( \begin{array}{ccc} 0& -4& 2\\-4& 8&-4\\-8&24+k&-14\end{array}\right )
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  3. #3
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    or compute the determinant.
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