Yadda za a yi da gano da determinant na matrix?

Gano da determinant na matrix da muhimmanci ba kawai ga mataki na mikakke aljabara: misali, tattalin arzikin amfani da wannan lissafi warware tsarin na mikakke lissafai da mahara unknowns suna yadu amfani da tattalin arziki matsaloli.

A ra'ayi na determinant

Determinant ko determinant na matrix da aka kira wani adadin daidai girma parallelepiped gina a kan ta jere vectors ko ginshikan. Lissafta wannan darajar kawai ga wani square matrix a cikin abin da yawan layuka da kuma ginshikan guda. Idan matrix mambobi - da lambar, da lambar da za su zama da determinants.

Lissafi na determinants

Ka tuna cewa akwai wasu dokokin da za su iya ƙwarai sauƙaƙe wannan lissafin.

Tun da determinant na matrix kunshi daya memba, shi ne guda kashi. Lissafi da determinant na biyu domin ba shi da wuya, shi ne isa da samfurin na diagonal mambobi dauki samfurin da abubuwa zubar a kan sakandare diagonal.

Ana kirga da determinant 3 game da mafi sauki hanyar gudanar a alwatika mulki. Don yin wannan, yi da wadannan matakai:

1. Mun sami samfurin na uku matrices na mambobin located a kan ta main diagonal.
2. Ninka ta uku mambobi da suke kan triangles, da kwasfa na waxanda suke a layi daya zuwa babban diagonal.
3. Maimaita na farko da na biyu mataki zuwa secondary diagonal.
4. Nemo Naira Miliyan Xari da sakamakon dabi'u a baya lissafin, da lambobin samu a cikin na uku sakin layi, za mu dauki wani mummunan darajar.

Don saukin ciyar gano da determinant na oda 4 kuma mafi girma girma, shi wajibi ne don la'akari da kaddarorin mallaki by duk determinants:

1. Tamanin da determinant ba ya canja bayan da transposition na matrix.
2. Musanya biyu m jere ko shafi take kaiwa zuwa wani canji a cikin alamar da determinant.
3. Idan matrix yana da biyu daidai layuka ko ginshikan, ko duk abin da abubuwa na shafi (Lines) sifili, ta determinant ne sifili.
4. Multiplication da matrix zuwa wani lamba take kaiwa zuwa kara na ta determinant a cikin wannan adadin sau.

Amfani da sama da kaddarorin sa shi sauki don gudanar da tabbatar da dalilin da determinant na matrix da sabani domin. Alal misali, yin amfani da oda rage Hanyar cikin abin da bazuwar daga cikin determinant kashi jere (shafi) yawaita da cofactor.

Wani Hanyar wanda muhimmanci simplifies gano da determinant matrix, shi ne ya kawo shi zuwa wani triangular tsari, lokacin da dukan abubuwa a karkashin babban diagonal ne sifili. A wannan yanayin, da determinant da aka lasafta a matsayin samfurin da lambobin positioned a kan wannan diagonal.

Kuma a karshe ina son a lura da cewa lissafin determinants, ko da yake shi kunshi wani alama sauki ilmin lissafi lissafin, duk da haka, na bukatar babba kula da kuma juriyarsu.