Rouché–Capelli theorem

theorem in linear algebra that a system of linear equations with n variables has solution(s) iff the rk(A) = rk([A|b]), and that if there are solutions, they form an affine space of dimension n−rk(A)
rdfs:label
"Rouché–Capelli theorem"@en
skos:altLabel
"Kronecker–Capelli theorem"@en
"Rouché–Fontené theorem"@en
"Rouché–Frobenius theorem"@en
schema:description
"theorem in linear algebra that a system of linear equations with n variables has solution(s) iff the rk(A) = rk([A|b]), and that if there are solutions, they form an affine space of dimension n−rk(A)"@en
schema:dateModified "2026-07-15T00:32:48+00:00"^^xsd:dateTime
schema:version 2517568796
wikibase:identifiers 4
wikibase:sitelinks 25
wikibase:statements 13
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wdt:P11514 "teorema-kronekera-kapelli-e59fb0"
wdt:P138 Eugène Rouché
Georges Fontené
Alfredo Capelli
Ferdinand Georg Frobenius
Leopold Kronecker
wdt:P2159 system of linear equations
wdt:P31 theorem
wdt:P361 list of theorems
wdt:P6104 WikiProject Mathematics
wdt:P646 "/m/0czdb75"
wdt:P7666 "kroneckerio-ir-capelli-teorema"
wdt:P9621 "teorema-di-rouche-capelli"
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