Answer
dim (Nul A) = 0
dim (Col A) = 3
Work Step by Step
We are given the matrix A = $\begin{bmatrix}
1 & -1 & 0 \\
0 & 4 & 7\\
0 & 0 &5\\
\end{bmatrix}$.
Notice first that the matrix is already given to us in echelon form.
Since each of the matrix's 3 columns has a pivot position, the dimension of Col A must be 3.
Then, since there are no free variables (no columns that do not contain a pivot), the dimension of Nul A must be 0.
