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Homework Help: Null space vs Col space dimension?

  1. May 29, 2010 #1
    I have a question in my linear algebra text that asks:

    Give integers p and q such that Nul A is a subspace of Rp and Col A is a subspace of Rq.

    What determines these values? Why are the values of p and q different between the Nul space and Col space? The matrix in question is a 3 x 4 matrix and the value for Col A was 3 and Nul A was 4.

    3 2 1 -5
    -9 -4 1 7
    9 2 -5 1

    Why are they different? I would have thought the dimension was just the number of entires in each column. How can Nul space be 4 dimensions when there are only 3 entries in the column vectors?
  2. jcsd
  3. May 29, 2010 #2


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    Staff Emeritus
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    Gold Member

    The null space is the kernel of the matrix. What is the domain of your matrix?
  4. May 29, 2010 #3
    What do you mean by kernel?
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