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    Vector Subspaces

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    What would a vector v in R4 such that:

    V(1,2,1,0) T V(1,0,-1,1) T V(0,2,0,-1) = <v>

    AND find scalars a,b,c,d such that

    <(1,2,1,0),(1,0,-1,1),(0,2,0,-1)> = <v>

    Please note:
    <v1,...,vk> denotes the vector subspace of Rn generated by the vectors v1,...,vk and that for scalars a1,...,an belonging to R,
    V(a1,...,an) = {x belonging to Rn : a1x1+...+anxn = 0}

    Also, T means intersection.

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    Solution Preview

    Let v=(x1,x2,x3,x4)
    Since V(1,2,1,0) T V(1,0,-1,1) T V(0,2,0,-1) = <v> , v belong to V(1,2,1,0) and ...

    Solution Summary

    Vector subspaces are investigated. The solution is well explained.