### 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 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

*25*(1), 297-302.

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*Communications in Algebra*, vol. 25, no. 1, pp. 297-302.

**Solvability of linear equations and rank-function.** / Prasad, K. Manjunatha.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Solvability of linear equations and rank-function

AU - Prasad, K. Manjunatha

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=25844520148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25844520148&partnerID=8YFLogxK

M3 - Article

VL - 25

SP - 297

EP - 302

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 1

ER -