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Nullspace, Column Space, and solution of system given only rref(A)

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose a 3 x 5 matrix A has row-reduced echelon form:
    [[1 2 0 0 5]
    [0 0 1 0 4]
    [0 0 0 1 3]]

    a. Describe NS(A)
    b. Describe CS(A)
    c. Suppose
    . [[2]
    . [3] [[-2]
    A [5] = [4] = b
    . [1] [3]]
    . [9]]

    To be clear, that's the original matrix A times the vector x = {2, 3, 5, 1, 9} to give us the vector b = {-2, 4, 3}.

    Find all solutions of the equation Ax = b

    2. Relevant equations



    3. The attempt at a solution

    I completed a) by finding the basis for the nullspace to be the set of the two following vectors

    {2, 1, 0, 0, 0} , {-5, 0, -4, -3, 1}

    I'm not really sure how to do part b) since I'm not given the original matrix A, just the rref(A)

    I have absolutely no idea how to do part c) since I'm not given the original matrix.

    Please Help!
     
  2. jcsd
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