192 W.Wang.J.Zhao Linear Algebra and its Applications 291 (1999)185-199 We get (-RTY)+2=0,O1-YTR-2,=0, 02191+Q2YTR01=0. Since -T is row M-1-invariant matrix,u is nonsingular.We obtain 2+z2YTR-=0 and y=02R+022YT=0. Hence e(R)-(6) If U is upper triangular for e()-(8) then it is easy from Lemma 3.1 to see e()=() Theorem 3.3.Let O satisfy the same assumptions as in Lemma 3.2,if w is the solution to (11),then the solution to (12)is given by w=w-ED-T(u-YTw): (16) with E and D given in Lemmas 3.1 and 3.2. Proof.Let ex=(6)c=() where s E R",S2E R-",is Mi-invariant matrix. Then Eq.(12)can be rewritten as mmw-r()-()儿 =mw(食()儿 (17)