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Math Help - Lin. Dep. Matrix

  1. #1
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    Lin. Dep. Matrix

    Find all values of a such that the set \{\left[ \begin {array}{c} a\\\noalign{\medskip}1\end {array} \right], \left[ \begin {array}{c} a+2\\\noalign{\medskip}a\end {array}\right]\} is linearly dependent.


    Work for this problem:

    We have \left[ \begin {array}{cc} a&a+2\\\noalign{\medskip}1&a\end {array}\right]

    Row 1 - Row 2 yields:

    \left[ \begin {array}{cc} a&a+2\\\noalign{\medskip}a-1&2\end {array}\right]

    Now not sure where to proceed.
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  2. #2
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    I believe a = -1 works just by playing with it, but I don't know how to tell if that's the only solution or if there are others. . . anyone ?!
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  3. #3
    Moo
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    Hello,

    I'm sorry no one is replying to your threads :s

    Hmm I'll try for this one. Seems easy

    Two vectors are linearly dependent if there are m and n different from 0 such that mu+nv=0. ---> mu=-nv.
    So you have to set a such that the coordinates in the matrices have a common ratio.

    \frac a1=\frac{a+2}{a}

    \implies a^2=a+2 \implies a^2-a-2=0

    so now find a


    Note : this is similar to finding a such that the matrix 2x2 you've got is non invertible (determinant = 0)
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