M’bukuli, tiona kuti njira ya Gaussian ndi chiyani, chifukwa chake ikufunika, komanso mfundo yake. Tidzawonetsanso pogwiritsa ntchito chitsanzo chothandiza momwe njirayo ingagwiritsire ntchito kuthetsa dongosolo la ma equation a mzere.
Kufotokozera kwa njira ya Gauss
Njira ya Gauss ndi njira yachikale yochotsera motsatizana zosintha zomwe zimagwiritsidwa ntchito kuthetsa. Amatchulidwa ndi katswiri wa masamu wa ku Germany Carl Friedrich Gauss (1777-1885).
Koma choyamba, tiyeni tikumbukire kuti SLAU ikhoza:
- khalani ndi yankho limodzi;
- kukhala ndi njira zambiri zopanda malire;
- kukhala osagwirizana, mwachitsanzo, kukhala opanda mayankho.
Zopindulitsa
Njira ya Gauss ndi njira yabwino yothetsera SLAE yomwe imaphatikizapo ma equation oposa atatu, komanso machitidwe omwe sali lalikulu.
Mfundo ya njira ya Gauss
Njirayi ili ndi njira zotsatirazi:
- Molunjika - matrix owonjezera omwe amagwirizana ndi dongosolo la equation, amachepetsedwa ndi njira yomwe ili pamwamba pa mizere kupita ku mawonekedwe apamwamba a katatu (opondapo), mwachitsanzo, pansi pa diagonal yayikulu iyenera kukhala ndi zinthu zofanana ndi ziro.
- mmbuyo - muzotsatira zake, zinthu zomwe zili pamwamba pa diagonal yayikulu zimayikidwanso ku zero (mawonedwe otsika katatu).
Chitsanzo cha yankho la SLAE
Tiyeni tithetse dongosolo la ma equation a mzere pansipa pogwiritsa ntchito njira ya Gauss.
Anakonza
1. Poyamba, timapereka SLAE mu mawonekedwe a matrix owonjezera.
2. Tsopano ntchito yathu ndikukhazikitsanso zinthu zonse pansi pa diagonal yayikulu. Zochita zina zimadalira matrix enieni, m'munsimu tidzafotokozera zomwe zimagwira ntchito pa nkhani yathu. Choyamba, timasintha mizere, motero timayika zinthu zawo zoyambirira mu dongosolo lokwera.
3. Chotsani mzere wachiwiri kawiri koyamba, ndipo kuchokera pachitatu - katatu woyamba.
4. Onjezani mzere wachiwiri ku mzere wachitatu.
5. Chotsani mzere wachiwiri kuchokera pamzere woyamba, ndipo nthawi yomweyo gawani mzere wachitatu ndi -10.
6. Gawo loyamba latha. Tsopano tiyenera kupeza zinthu zopanda pake pamwamba pa diagonal yayikulu. Kuti muchite izi, chotsani chachitatu chochulukitsa ndi 7 kuchokera pamzere woyamba, ndikuwonjezera chachitatu chochulukitsa ndi 5 mpaka chachiwiri.
7. Matrix omaliza owonjezera amawoneka motere:
8. Zimagwirizana ndi dongosolo la ma equation:
Yankho: mizu SLAU: x = 2, y = 3, z = 1.