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Homework Help: Find unknown element in a matrix

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Find all values of a for which the columns of the matrix are linearly dependent.

    [tex]
    \left( {\begin{array}{*{20}c}
    2 & 0 & 8 \\
    { - 4} & 7 & a \\
    1 & { - 3} & 4 \\
    \end{array}} \right)
    [/tex]


    2. Relevant equations



    3. The attempt at a solution
    So I took of rref of the matrix and found

    [tex]
    \left( {\begin{array}{*{20}c}
    1 & 0 & 4 \\
    { - 0} & 1 & 0 \\
    0 & { 0} & a+16 \\
    \end{array}} \right)
    [/tex]

    So then I have
    a+16=0
    a = -16


    So that gives me 1 value which makes the columns of the matrix linearly dependent, but how do I find the other ones, or even know if more exist?

    Thanks
     
  2. jcsd
  3. Oct 18, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You've got it. There is just the one value, a=(-16). Otherwise the columns of the reduced matrix are linearly independent.
     
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