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Matrices hyperplane

  1. Nov 22, 2004 #1
    Please Help!

    I can't figure this out no matter how many times I try. Please can someone help me with this homework question?:

    Let:

    v1=[1]
    [1]
    [0]
    [0]

    v2=[1]
    [0]
    [1]
    [0]

    v3=[1]
    [0]
    [0]
    [1]

    v4=[1]
    [1]
    [1]
    [1]

    and let
    V= Span{v1,v2,v3) intersection Span{v4}^perp

    (sorry i don't know how to type the symbols for intersection and perpenducular)

    In other words, V is the set of vectors x in the hyperplane Span{v1,v2,v3) which also satisfy the equation v4 · x = 0, i.e. x1+x2+x3+x4=0.

    a) Find a matrix A such that V=N(A)
    b) Find a matrix B such that V=C(B)

    Thanks in advance!
     
    Last edited: Nov 22, 2004
  2. jcsd
  3. Nov 22, 2004 #2
    What do V = N(A) and V = C(B) mean ?
     
  4. Nov 23, 2004 #3
    N(A) is the nullspace of A.
    C(B) is the column space of B.

    The question asks to find a matrix A such that the vector space V equals the nullspace of A, and to find a matrix B such that the vector space V equals the column space of B.
     
  5. Nov 23, 2004 #4
    I think you got your terminology a bit mixed up, they want you to find matrices A and B such that V *spans* the nullspace of A and V *spans* the nullspace of in other words find a matrix such that

    AV = 0 where is the 0 vector [0 0 0 0] (vertically though)

    BV = span(V)

    Let me given you a hint: what is the span of the matrix consisting of the vectors [v1 v2 v3 v4] ? Do the vectors happen to be linearly independent? If so what would their span be ? If not, what set of vectors forms a linearly independent set ? Now that you know the span of the set, can't you find its kernel? What would that mean about the nullspace?
     
    Last edited: Nov 23, 2004
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