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

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?