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Math Help - LinAlg - a few questions?

  1. #1
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    LinAlg - a few questions?

    so i have the matrices
    [-12
    16
    -13] = A

    (it is a 3x1 matrix)

    [-3
    5
    -4] = B

    [-3
    3
    -3] = C

    Determine whether A, B, and C are linearly independent
    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 = 0

    my teacher told me to do something with C1, C2... Cn... but I have no idea what that means! haha

    thanks so much in advance
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  2. #2
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    You can check that A-2B-2C=0
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  3. #3
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    how did you do it?
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  4. #4
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    Quote Originally Posted by watchmath View Post
    You can check that A-2B-2C=0
    Actually A - 2B - 2C = \left( \begin{gathered}<br />
0 \hfill \\<br />
0 \hfill \\<br />
1 \hfill \\ <br />
\end{gathered} \right).
    In fact, the three are linearly independent.
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  5. #5
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    haha i kinda figured when i put it in and got it wrong...
    and then it took me a little while to actually figure it out!
    thanks plato =)
    so now i have another question
    and i've reduced the matrix down to

    [ 1 0 -2 0
    0 1 2 0
    0 0 0 0]

    and this is also testing for linear indepedence
    so i know that this one is linearly dependent
    but i have to write another non-trivial solution in the form
    ___A+ ____B+____C= 0
    so how would I do that?
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  6. #6
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    Quote Originally Posted by eiktmywib View Post
    so now i have another question
    and i've reduced the matrix down to
    [ 1 0 -2 0
    0 1 2 0
    0 0 0 0]
    What matrix? You must give the complete question.
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  7. #7
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    oh sorry =(
    A=[-2, -7, -1]
    B=[-2, 4, -3]
    C=[0,6,-4]

    and i'm supposed to determine if they're linearly depedent or independent
    The vectors were written horizontally this time, as they often are in books, but that is just to save space. The problem is the same as if the vectors were written vertically.
    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.
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