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Homework Help: Spaningset theorem

  1. Jun 14, 2005 #1
    Spaning set theorem (new Question)

    Hi

    I have a couple of questions regarding an assignment which deals with the spanning set theorem.

    Hope You can help

    The matrix [tex]A = [a1 \ a2 \ a3 \ a4 \ a5] = \left[ \begin{array}{ccccc} 1 & 0 & 0 & 1 & -1 \\ 0 & 1 & 1 & 2 & 0 \\ 1 & 0 & 0 & 1 & 2 \\ -1 & 2 & 2 & 3 & 1 \end{array} \right][/tex]

    a) First I determin the rank of A rank(A) = 3

    The dimension of Null A: dim (Null A) = 2

    b) Determin a basis for A's column space.

    I do this using the spanning set theorem.

    Since a3 = a2, a4 = 2a2 + a1 then

    B(ColA) = sp{a1,a2, a5} According to the theorem.

    c) Next the basis for the B(Null A).

    First I row reduce A and then up and write up the set of solutions for A which results in the set B(Null A) = span{(0,-1,1,0) , (1,-2,0,1)}

    Is that the correct approach ??

    d) There is a vector x = a1 + a2 + a3 + a4 + a5. I'm tasked with showing that this vector belongs to Col A. Finally I'm tasked with finding the vector x with respect to the basis B.

    I need some assistance is solving c) and d) therefore I hope there is somebody out there who can guide me :-)

    Sincerely and Best Regards,

    Fred



    /Fred
     
    Last edited: Jun 14, 2005
  2. jcsd
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