<s>
A	O
monotone	B-Algorithm
matrix	I-Algorithm
is	O
nonsingular	O
.	O
</s>
<s>
Proof	O
:	O
Let	O
be	O
a	O
monotone	B-Algorithm
matrix	I-Algorithm
and	O
assume	O
there	O
exists	O
with	O
.	O
</s>
<s>
In	O
fact	O
,	O
this	O
matrix	O
is	O
an	O
M-matrix	B-Algorithm
(	O
i.e.	O
,	O
a	O
monotone	O
L-matrix	B-Algorithm
)	O
.	O
</s>
<s>
Note	O
,	O
however	O
,	O
that	O
not	O
all	O
monotone	B-Algorithm
matrices	I-Algorithm
are	O
M-matrices	B-Algorithm
.	O
</s>
