"2"^^ . . "J\u00E1dro matice"@cs . . "13791364"^^ . "nulov\u00E9m prostoru"@cs . . . . "j\u00E1dro matice"@cs . "Definice: Mno\u017Eina v\u0161ech \u0159e\u0161en\u00ED homogenn\u00ED soustavy line\u00E1rn\u00EDch rovnic Ax=o se naz\u00FDv\u00E1 j\u00E1dro matice A nebo tak\u00E9 nulov\u00FD prostor matice A."@cs . "1055260"^^ . "j\u00E1drem"@cs . . . "Definice: Mno\u017Eina v\u0161ech \u0159e\u0161en\u00ED homogenn\u00ED soustavy line\u00E1rn\u00EDch rovnic Ax=o se naz\u00FDv\u00E1 j\u00E1dro matice A nebo tak\u00E9 nulov\u00FD prostor matice A. Ozna\u010Dujeme ji Ker A.Pozorov\u00E1n\u00ED 1: Jsou-li u a w dv\u011B \u0159e\u0161en\u00ED soustavy line\u00E1rn\u00EDch rovnic Ax = b, pak w - u je \u0159e\u0161en\u00EDm soustavy Ax = o.Pozorov\u00E1n\u00ED 2: Je-li u \u0159e\u0161en\u00EDm soustavy Ax = b a v \u0159e\u0161en\u00ED p\u0159\u00EDslu\u0161n\u011B homogen\u00ED soustavy Ax = o, pak u + v je tak\u00E9 \u0159e\u0161en\u00EDm soustavy Ax = b.V\u011Bta: Je-li u jedno pevn\u011B zvolen\u00E9 partikul\u00E1rn\u00ED \u0159e\u0161en\u00ED soustavy line\u00E1rn\u00EDch rovnic Ax=b nad t\u011Blesem T, pak se mno\u017Eina v\u0161ech \u0159e\u0161en\u00ED t\u00E9to soustavy rovn\u00E1 {u+v : v \u2208 Ker A} = u + Ker A.D\u016Fkaz: Je-li w \u0159e\u0161en\u00ED soustavy Ax=b, pak (w - u) \u2208 Ker A (podle pozorov\u00E1n\u00ED 1) a tedy w = u + (w - u) \u2208 {u + v : v \u2208 Ker A}. Naopak pro libovoln\u00E9 v \u2208 Ker A je u + v \u0159e\u0161en\u00EDm soustavy Ax=b (podle pozorov\u00E1n\u00ED 2)."@cs . "974"^^ . .