I've been sitting on this practice question for a while but haven't been able to make any progress. Thanks in advance for any help.
Below is an $n \times m$ matrix over $\mathbb{R}$:
$$A= \begin{bmatrix}a_{1,1}& \dots &a_{1,n}\\ \vdots & \ddots & \vdots \\ a_{m,1}&...&a_{m,n}\end{bmatrix} \text{with} \ a_{i,j} = i + j \ \text{for all} \ i \in {1,..m}, \ j\in{1,...n}.$$
Determine the row and column rank of the matrix $A$ for any $n,m > 0$.
How do I go about this question? I know the rank of a matrix is the number of linearly independent rows or columns, but I don't really know how to apply that to this matrix.
P.S: please excuse my poor formatting.
Hint: Subtracting any two consecutive rows gives you the vector $(1,1,\dots,1)$. Conclude that the rank of the matrix is at most $2$.