Answer
p=3, q=4
Work Step by Step
Because A has 3 columns, Nul A is a subspace of $R^3$ and because A has 4 rows, Col A is a subspace of $R^4$. This is because a vector $x$ such that $Ax=0$ must have 3 entries, meaning it is in $R^3$ and every vector in Col A must have 4 entries because each column vector in A has 4 entries.
