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Math Help - Find k in a 3x3 matrix

  1. #1
    Member mybrohshi5's Avatar
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    Find k in a 3x3 matrix

    Find K such that the matrix

    <br />
\begin{bmatrix}-2 & -1 & 3 \\6 & 5 & -5 \\ 10+k & 4 & -2\end{bmatrix}<br />

    is singular.


    I have no idea how to go about solving this. Can anyone lead me in the right direction. it would be much appreciated. Thank you
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  2. #2
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    Joined
    Feb 2010
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    jordan
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    Quote Originally Posted by mybrohshi5 View Post
    Find K such that the matrix

    <br />
\begin{bmatrix}-2 & -1 & 3 \\6 & 5 & -5 \\ 10+k & 4 & -2\end{bmatrix}<br />

    is singular.


    I have no idea how to go about solving this. Can anyone lead me in the right direction. it would be much appreciated. Thank you

    A matrix is singular iff its determinant is 0

    let your matrix called A

    then det (A) =0 since A is singular

    det (A)= (-2*5*-2)+(-1*-5*(10+k))+(72)-(150+15k)-(40)-(12)=0

    (20)+(50+5k)+(72)-(150+15k)-(40)-(12)=0

    -100-10k+40=0

    -60-10k=0


    k=-6
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