Null space vs Col space dimension?

  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. Office_Shredder

    Office_Shredder 4,487
    Staff Emeritus
    Science Advisor
    Gold Member

    The null space is the kernel of the matrix. What is the domain of your matrix?
  4. What do you mean by kernel?
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