  We study metrically projective and metrically free matricially normed spaces.
We describe these spaces in terms of a special space $\widehat M_n$, the space
of $n\times n$ matrices, endowed with a special matrix-norm. We show that
metrically free matricially normed spaces are matricial $\ell_1$-sums of some
distinguished families of matricially normed spaces $\widehat M_n$, whereas
metrically projective matricially normed spaces are complete direct summands of
matricial $\ell_1$-sums of arbitrary families of the spaces $\widehat M_n$. At
the end we specify the underlying normed space of $\widehat M_n$ and show that
the spaces $\widehat M_n$; $n>1$ do not belong to any of the classes $L^p$;
$p\in [1,\infty]$, introduced by Effros and Ruan. However, in a certain sense
the behavior of $\widehat M_n$ resembles that of $L^1$-spaces.
