  A finite or infinite matrix $A$ is image partition regular provided that
whenever $\mathbb N$ is finitely colored, there must be some $\vec{x}$ with
entries from $\mathbb N$ such that all entries of $A\vec{x}$ are in some color
class. In [6], it was proved that the diagonal sum of a finite and an infinite
image partition regular matrix is also image partition regular. It was also
shown there that centrally image partition regular matrices are closed under
diagonal sum. Using Theorem 3.3 of [2], one can conclude that diagonal sum of
two infinite image partition regular matrices may not be image partition
regular. In this paper we shall study the image partition regularity of
diagonal sum of some infinite image partition regular matrices. In many cases
it will produce more infinite image partition regular matrices.
