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?