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Thread: Linear Combination and Span?

  1. #1
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    Linear Combination and Span? [Solved]

    How would you show that the vectors (1,1,0) (1,0,1) and (0,1,1) generate F^3?

    Do you simply put them in the matrix and solve the matrix or?
    Last edited by leungsta; Sep 13th 2008 at 05:48 PM.
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  2. #2
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    Quote Originally Posted by leungsta View Post
    How would you show that the vectors (1,1,0) (1,0,1) and (0,1,1) generate F^3?

    Do you simply put them in the matrix and solve the matrix or?
    Since F^3 (whatever that is) has dimension three it means if you can show {(1,1,0),(1,0,1),(0,1,1)} are linearly independent it would mean they must spam the space.
    Now say a(1,1,0)+b(1,0,1)+c(0,1,1) = (0,0,0).
    This means,
    a+b = 0
    a+c=0
    b+c=0
    Now argue that a=b=c=0.
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  3. #3
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    Thanks! Got the answer
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