1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find unknown element in a matrix
  1. Matrix with 2 unknowns (Replies: 3)

Loading...