Vector space/Product/Dimension/Exercise

Let ${}K$ be a field, and let ${}V$ and ${}W$ be two finite-dimensional ${}K$-vector spaces with

${}\dim _{K}{\left(V\right)}=n\,$

and

${}\dim _{K}{\left(W\right)}=m\,.$

What is the dimension of the Cartesian product ${}V\times W$?

To solution