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Basis for null space, row space, dimension

  1. Nov 9, 2008 #1
    1. The problem statement, all variables and given/known data
    What are

    the basis for the row space and null space for the following matrix? Find the dimension of RS, dim of NS.

    [1 -2 4 1]
    [3 1 -3 -1]
    [5 -3 5 1]

    2. Relevant equations

    dim RS + dim NS = # of columns

    3. The attempt at a solution

    I reduced the matrix into row echelon form and tried to determine everything, but in vain.
  2. jcsd
  3. Nov 9, 2008 #2
    Come on, this is a pretty fundamental question. If you want to find the row space, you are going to want to row reduce the matrix and use all the nonzero rows as a basis.

    To find the null space, set Ax = 0 and solve [ A 0] and right the solution in parametric form. Take the vectors you have in parametric form as your basis.
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