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Stability conditions for flexible systems are given in terms of relative imprecision and size of determinants. We then apply the explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure to find the solution of flexible systems, keeping track of the error terms at every stage. The solution respects the original imprecisions in the right-hand side and is the same as the one given by Cramer\u2019s rule.<\/jats:p>","DOI":"10.1515\/spma-2022-0168","type":"journal-article","created":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T23:03:33Z","timestamp":1654902213000},"page":"366-393","source":"Crossref","is-referenced-by-count":0,"title":["The explicit formula for Gauss-Jordan elimination applied to flexible systems"],"prefix":"10.1515","volume":"10","author":[{"given":"Nam Van","family":"Tran","sequence":"first","affiliation":[{"name":"Faculty of Applied Sciences, HCMC University of Technology and Education , Ho Chi Minh City , Vietnam"}]},{"given":"J\u00falia","family":"Justino","sequence":"additional","affiliation":[{"name":"Set\u00fabal School of Technology, Polytechnic Institute of Set\u00fabal , Set\u00fabal , Portugal"},{"name":"Research Center in Mathematics and Applications, University of \u00c9vora , \u00c9vora , Portugal"},{"name":"Centre for Energy and Environment Research, Polytechnic Institute of Set\u00fabal , Set\u00fabal , Portugal"}]},{"given":"Imme van den","family":"Berg","sequence":"additional","affiliation":[{"name":"Research Center in Mathematics and Applications, University of \u00c9vora , \u00c9vora , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2022,6,10]]},"reference":[{"key":"2022071310194436094_j_spma-2022-0168_ref_001","doi-asserted-by":"crossref","unstructured":"J. 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