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These vectors are linear dependant, but i'm confused on their non trivial relationshi

  1. Dec 11, 2005 #1
    Hello everyone, i'm finishing up some matrices review and im' confused on this question i have the matrix:
    -1 -3 -1 2
    5 13 3 -8
    3 10 9 -8
    1 4 7 -4

    I row reduced got this:
    1 0 0 3/5
    0 1 0 -4/5
    0 0 1 -1/5
    0 0 0 0

    So you can see that this isn't a basis due to column 5 not being 0 0 0 1, but what does this mean the questions says:
    If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.
    ?A + ?B + ?C + ?D = 0.
    I tried 1 1 1 3/5
    1 1 1 0, i tried actually 14 times, all of them are wrong hah, any help?>
  2. jcsd
  3. Dec 11, 2005 #2

    matt grime

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    Did you record the row operations that you used? Because they tell you the relationship, the reduced row of zeroes is a linear combination of the 4 rows, just recall what the combination is.
  4. Dec 11, 2005 #3
    I used a Ti-83 calculator to find the row reduction, he said to use them for these problems!
  5. Dec 11, 2005 #4


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    You know how to solve a homogeneous system? If A is your matrix of column vectors, a non-trivial solution to the homogeneous system AX=0 will give you a non-trivial linear relation between your vectors.

    AX is just a linear combination of the columns of A after all.

    edit-are you concerned with a linear combination of the rows or the columns of your matrix? matt and i answered the different interpretations (in that order).
    Last edited: Dec 11, 2005
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