# A NOTE ON PARTIAL SIGN-SOLVABILITY

• Hwang, Suk-Geun (Department of Mathematics Education, Kyungpook National University) ;
• Park, Jin-Woo (Department of Mathematics Education, Kyungpook National University)
• Published : 2006.08.01
• 69 8

#### Abstract

In this paper we prove that if AX=b is a partial sign-solvable linear system with A being sign non-singular matrix and if ${\alpha}=\{j:\;x_j\;is\;sign-determined\;by\; Ax=b\}, then$A_{\alpha}X_{\alpha}=b_{\alpha}$is a sign-solvable linear system, where$A_{\alpha}$denotes the submatrix of A occupying rows and columns in o and xo and be are subvectors of x and b whose components lie in${\alpha}$. For a sign non-singular matrix A, let$A_l,\;...,A_{\kappa}$be the fully indecomposable components of A and let${\alpha}_i$denote the set of row numbers of$A_r,\;r=1,\;...,\;k$. We also show that if$A_x=b$is a partial sign-solvable linear system, then, for$r=1,\;...,\;k$, if one of the components of xor is a fixed zero solution of Ax=b, then so are all the components of x_{{\alpha}r}$.

#### Keywords

sign-solvable linear system;partial sign-solvable linear system

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