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Math Help - Spanning set.

  1. #1
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    Spanning set.

    a) Show that the set of vectors {u1 = <1 2 -1>, u2 = <-1 -1 0>, u3= <2 5 4>} spans R^3

    b)Express the vector v = <1 3 -2> in terms of the spanning set in part a).

    I already answered a), I just don't know how to answer b)

    By expressing does that mean I should just include the vector v in the set of given vectors? I'm not really sure with this one. Please help me. thanks!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by cookiejar View Post
    a) Show that the set of vectors {u1 = <1 2 -1>, u2 = <-1 -1 0>, u3= <2 5 4>} spans R^3

    b)Express the vector v = <1 3 -2> in terms of the spanning set in part a).

    I already answered a), I just don't know how to answer b)

    By expressing does that mean I should just include the vector v in the set of given vectors? I'm not really sure with this one. Please help me. thanks!
    Reduce the augmented matrix \begin{bmatrix}1 &-1 & 2 & 1\\ 2 & -1 & 5 & 3\\ -1 & 0 & 4 & -2\end{bmatrix} and you'll find the constants a,b,c such that a\left<1,2,-1\right>+b\left<-1,-1,0\right>+c\left<2,5,4\right>=\left<1,3,-2\right>
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  3. #3
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    So, I'll just solve the constants a, b, c to answer b)? I didn't think of that... but, Thanks anyway!
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