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