### Abstract

In this paper, we consider an m × n regular matrix A over a commutative ring A (-a matrix whose range is direct summand of A ^{m}) and a necessary and sufficient condition in terms of determinantal rank is obtained for solvability of Ax = b. In the light of this result we define rank-function for matrices.

Original language | English |
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Pages (from-to) | 297-302 |

Number of pages | 6 |

Journal | Communications in Algebra |

Volume | 25 |

Issue number | 1 |

Publication status | Published - 1997 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Prasad, K. M. (1997). Solvability of linear equations and rank-function.

*Communications in Algebra*,*25*(1), 297-302.