Gauss nzira yeSLAE mhinduro

Mubhuku rino, tichaona kuti nzira yeGaussian chii, nei ichidiwa, uye kuti chii chiri musimboti wayo. Isu ticharatidzawo tichishandisa muenzaniso unoshanda kuti nzira yacho ingashandiswa sei kugadzirisa hurongwa hwemitsetse equation.

Tsanangudzo yeGauss nzira

Gauss nzira ndiyo yemhando yepamusoro nzira yekutevedzana kubviswa kwezvakasiyana zvinoshandiswa kugadzirisa. Inotumidzwa zita remuGerman nyanzvi yemasvomhu Carl Friedrich Gauss (1777-1885).

Asi chekutanga, ngatiyeukei kuti SLAU inogona:

• iva nemhinduro imwe chete;
• kuva nehuwandu husingagumi hwezvigadziriso;
• kusapindirana, kureva kusava nemhinduro.

Zvibereko zvinoshanda

Iyo Gauss nzira inzira yakanaka yekugadzirisa SLAE inosanganisira anopfuura matatu mutsara equations, pamwe nemasisitimu asina mativi.

Nheyo yeGauss nzira

Iyo nzira inosanganisira matanho anotevera:

1. kururamiswa - the augmented matrix inoenderana nehurongwa hweequation, inoderedzwa nenzira iri pamusoro pemitsara kusvika kune yepamusoro triangular (yakatsika) fomu, kureva pasi peiyo diagonal huru inofanira kuva chete zvinhu zvakaenzana ne zero.
2. shure - mune inoguma matrix, zvinhu zviri pamusoro peiyo diagonal huru zvakare yakaiswa kune zero (yakaderera katatu maonero).

SLAE mhinduro muenzaniso

Ngatigadzirise sisitimu yemutsara equation pazasi tichishandisa nzira yeGauss.

mhinduro

1. Kutanga, tinopa SLAE muchimiro chekuwedzera matrix.

2. Iye zvino basa redu nderekugadzirisa zvinhu zvose pasi pe diagonal huru. Zvimwe zviito zvinoenderana nematrix chaiwo, pazasi isu tichatsanangura izvo zvinoshanda kune yedu kesi. Kutanga, tinochinjanisa mitsetse, nokudaro tichiisa zvinhu zvadzo zvekutanga mukukwira kurongeka.

3. Bvisa kubva pamutsara wechipiri kaviri yekutanga, uye kubva kune wechitatu - katatu wekutanga.

4. Wedzera mutsara wechipiri kumutsara wechitatu.

5. Bvisa mutsara wechipiri kubva pamutsara wekutanga, uye panguva imwechete ugovane mutsara wechitatu ne -10.

6. Danho rekutanga rinopedzwa. Iye zvino isu tinoda kuwana izvo zvisina chinhu pamusoro peiyo huru diagonal. Kuti uite izvi, bvisa wechitatu wakapetwa ne7 kubva pamutsara wekutanga, uye wowedzera wechitatu wakapetwa ne5 kune wechipiri.

7. Yekupedzisira yakawedzerwa matrix inoita seizvi:

8. Inofambirana nehurongwa hweequations:

Pindura: mudzi SLAU: x = 2, y = 3, z = 1.