I spend lot of hours on this problem, but now I'm givin it up.
As you can read in the title, the problem is about proving on R (I mean the calculation program) that the Moore-Penrose Pseudo-Inverse of this specific matrix
$$ \begin{matrix} 1 & 2 & 3 \\ 1 & 2 & 3 \\ 1 & 2 & 3 \\ \end{matrix} $$
can be calculate by limiting (as it is written on Wikipedia on that page: https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse#Limit_relations).
Can someone help me? If it is possible also with some calculations on R.
Thanks!