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!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

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

Have something to add?



Similar Discussions: These vectors are linear dependant, but i'm confused on their non trivial relationshi
Loading...