Ukuthakazelisa kuMlobi we-OpenOffice. Umhlahlandlela Wokuqala Osheshayo

Ikhono lokuxazulula izinhlelo zama-equations lingasetshenziswa kakhulu esikoleni, kodwa futhi ekusebenzeni. Ngesikhathi esifanayo, akuwona wonke umsebenzisi we-PC owazi ukuthi i-Excel inezixazululo zayo zokulingana okulinganayo. Ake sithole ukuthi sisebenzisa kanjani le-toolkit yamathuluzi wokucubungula ukufeza lo msebenzi ngezindlela ezihlukahlukene.

Izixazululo

Noma yikuphi ukulingana kungacatshangwa kuphela lapho izimpande zayo zitholakala. Ku-Excel, kunezinketho eziningi zokuthola izimpande. Ake sibheke ngamunye wabo.

Indlela 1: I-Matrix Method

Indlela evamile kakhulu yokuxazulula uhlelo lokulingana okulinganayo nama-Excel amathuluzi ukusebenzisa indlela ye-matrix. Ihlanganisa ekwakheni i-matrix kusukela kuma-coefficients of expressions, bese ekwakheni i-matrix ehlane. Ake sizame ukusebenzisa le ndlela ukuxazulula uhlelo olulandelayo lokulinganisa:


14x1+2x2+8x4=218
7x1-3x2+5x3+12x4=213
5x1+x2-2x3+4x4=83
6x1+2x2+x3-3x4=21

1. Sigcwalisa i-matrix ngezinombolo eziyi-coefficients ze-equation. Lezi zinamba kufanele zihlelwe ngokulandelana ngokulandelana, kucatshangelwa indawo yempande ngayinye abayibhalisa ngayo. Uma ngenye indlela inkulumo eyodwa yezimpande ayitholakali, ngakho-ke kulesi cala i-coefficient ibhekwa njengelingana no-zero. Uma i-coefficient ingaboniswa ku-equation, kodwa izimpande ezihambelanayo zikhona, kubhekwa ukuthi i-coefficient ilingana 1. Chaza ithebula eliphethwe njengevot A.



2. Ngokwehlukana, sibhala amanani emva kwesibonakaliso esifanayo. Chaza ngegama elivamile njenge-vector B.



3. Manje, ukuze uthole izimpande ze-equation, okokuqala, sidinga ukuthola i-matrix, okungahambisani nalowo okhona. Ngenhlanhla, ku-Excel kukhona opharetha okhethekile oklanyelwe ukuxazulula le nkinga. Kubizwa MOBR. I-syntax elula:

   = MBR (i-array)

   Ukuphikisana "Uhlu" - lokhu, eqinisweni, ikheli letafula lomthombo.

   Ngakho-ke, sikhetha eshadini isifunda samangqamuzana angenalutho, esilingana nosayizi ohlangene nobubanzi bokuqala. Chofoza inkinobho "Faka umsebenzi"itholakala eduze kwebha yefomula.



4. Ukugijima Amakhosi omsebenzi. Iya kusigaba "Isibalo". Kuloluhlu sibheke igama "I-MOBR". Ngemuva kokuthi itholakala, khetha bese uchofoza inkinobho. "Kulungile".



5. Iwindi lempikiswano yokusebenza iqala. MOBR. Inensimu eyodwa kuphela ngenombolo yezimpikiswano - "Uhlu". Lapha udinga ukucacisa ikheli letafula lethu. Ngale njongo, setha isikhombisi kule nsimu. Khona-ke sibamba inkinobho yesinxele segundane bese ukhetha indawo eshadini lapho i-matrix ikhona khona. Njengoba ungabona, idatha ku-izixhumanisi zendawo ifakwa ngokuzenzakalelayo efasiteleni. Emva kwalokhu umsebenzi usuqedile, okusobala kakhulu kungaba ukuchofoza inkinobho. "Kulungile"kodwa ungasheshi. Iqiniso liwukuthi ukuchofoza le nkinobho kufana nokusebenzisa umyalo Ngena. Kodwa uma usebenzisa ama-arrays ngemuva kokuqeda okokufaka kwefomula, ungacindezeli inkinobho. Ngenafuthi ukhiqize isethi yamakhi okunciphisa Ctrl + Shift + Faka. Yenza lo msebenzi.



6. Ngakho, emva kwalokhu, lolu hlelo lwenza izibalo kanye nomkhiqizo endaweni ekhethiwe ngaphambili sinomthelela we-matrix.



7. Manje sizodinga ukwandisa i-matrix engenayo nge-matrix. Beliqukethe ikholomu eyodwa yamagugu akhiwe ngemuva kwesibonakaliso kufana ezinkulumweni. Ngoba ukuphindaphinda kwamatafula ku-Excel kunomsebenzi ohlukile, obizwa ngokuthi Umama. Lesi sitatimende sine-syntax elandelayo:

   = I-MUMNOGUE (i-Array1; i-Array2)

   Khetha ububanzi, esimweni sethu esakhiwa ngamaseli amane. Bese ugijima futhi Umsebenzi weWebhungokuchofoza isithonjana "Faka umsebenzi".



8. Esikhathini "Isibalo"egijima Amakhosi omsebenzikhetha igama "UMUMNOZH" bese uchofoza inkinobho "Kulungile".



9. Iwindi lempikiswano yokusebenza ivuliwe. Umama. Ensimini "Massive1" faka izixhumanisi ze-matrix yethu engenayo. Ukuze wenze lokhu, njengesikhathi sokugcina, setha isikhangiso ensimini futhi inkinobho yegundane lesokunxele egcinwe phansi, khetha ithebula elihambelanayo ne-cursor. Isenzo esifanayo senziwa ukwenza izixhumanisi endle "Massiv2", kuphela lesi sikhathi sikhetha amanani ekholomu. B. Ngemuva kokuthi izenzo ezithathwe ngenhla zithathwe, futhi asikho esheshayo ukucindezela inkinobho "Kulungile" noma ukhiye Ngena, bese uthayipha inhlanganisela yokhiye Ctrl + Shift + Faka.



10. Ngemuva kwalesi senzo, izimpande ze-equation zivela kuseli elikhethiwe ngaphambilini: X1, X2, X3 futhi X4. Zizohlelwa ngochungechunge. Ngakho-ke, singasho ukuthi sesixazulule le nqubo. Ukuze uqinisekise ukufaneleka kwesisombululo, kwanele ukufaka izimpendulo ezinikeziwe kwisistimu yokukhulumisana yasekuqaleni esikhundleni sezimpande ezihambelanayo. Uma ukulingana kugcinwa, lokhu kusho ukuthi uhlelo olunikeziwe lwezolinganiso luxazululwa ngendlela efanele.

Isifundo: I-Excel Reverse Matrix

Indlela 2: ukukhethwa kwemingcele

Indlela yesibili eyaziwa yokuxazulula uhlelo lwe-equations ku-Excel yindlela yokukhetha i-parameter. Okuyinhloko yale ndlela ukucinga okuphambene nalokho. Okusho ukuthi, ngokusekelwe kumphumela owaziwayo, sifuna ingxabano engaziwa. Masisebenzise isibalo se-quadratic njengesibonelo.

3x ^ 2 + 4x-132 = 0

1. Yamukela inani x ukulingana 0. Bala inani elihambelana nalo f (x)ngokusebenzisa ifomula elandelayo:

   = 3 * x ^ 2 + 4 * x-132

   Esikhundleni sokubaluleka "X" faka ikheli leseli lapho inombolo ikhona khona 0uthathwe ngathi x.



2. Iya kuthebhu "Idatha". Sicindezela inkinobho "Ukuhlaziywa" kuthiwani uma. Le nkinobho ifakwa ebhodini ebhokisini lamathuluzi. "Ukusebenza nedatha". Uhlu lokudonsa luvuleka. Khetha isikhundla kuso "Ukukhetha kwepharamitha ...".



3. Iwindi lokukhetha ipharamitha liqala. Njengoba ungabona, iqukethe amasimu amathathu. Ensimini "Faka esitokisini" ucacise ikheli leseli lapho ifomula itholakala khona f (x)sibalwa ngathi kancane kancane. Ensimini "Value" faka inombolo "0". Ensimini "Ukuguqula Amanani" ucacise ikheli leseli lapho inani likhona khona xngaphambilini esamukelwe thina 0. Ngemva kokwenza lezi zenzo, chofoza inkinobho "Kulungile".



4. Ngemuva kwalokho, i-Excel izokwenza ukubala ngokusebenzisa ukukhetha kwepharamitha. Lokhu kuzokwazisa iwindi lelwazi elibonakalayo. Kufanele uchofoze inkinobho "Kulungile".



5. Umphumela wokubala wempande ye-equation izoba esitokisini esabanike ensimini "Ukuguqula Amanani". Esikhathini sethu, njengoba sibona x uzolingana 6.

Lo mphumela ungabuye uhlolwe ngokufaka esikhundleni salesi silinganiso kwinkulumo exazululwe esikhundleni senani x.

Isifundo: Ukukhethwa kwepharamitha ye-Excel

Indlela yesithathu: Indlela ye-Cramer

Manje sizozama ukuxazulula uhlelo lwe-equations ngendlela ye-Kramer. Isibonelo, ake sithathe isimiso esifanayo esasetshenziswa kuwo Indlela 1:


14x1+2x2+8x4=218
7x1-3x2+5x3+12x4=213
5x1+x2-2x3+4x4=83
6x1+2x2+x3-3x4=21

1. Njengendlela yokuqala, senza i-matrix A kusukela kuma-coefficients of equations kanye netafula B yamagugu alandela isibonakaliso kufana.



2. Ngaphezu kwalokho senza amatafula amane. Ngamunye wabo ikhophi ye-matrix. A, kuphela lamakhophi anakho ikholomu elilodwa elihlelwe yithebula B. Etafuleni lokuqala yikholomu yokuqala, etafuleni lesibili kungesibili, njalonjalo.



3. Manje sidinga ukubala izinqumo kuzo zonke lezi zibhebhe. Uhlelo lwe-equations luyoba nezixazululo kuphela uma zonke izici zinenani ngaphandle kwezinga. Ukubala leli xabiso ku-Excel futhi kukhona umsebenzi ohlukile - MEPRED. I-syntax yalesi sitatimende kanje:

   = MEPRED (i-array)

   Ngakho, njengomsebenzi MOBR, ukuphikisana okuwukuphela kokubhekisela kwetafula kusetshenzwa.

   Ngakho, khetha iseli lapho i-matrix yokuqala ikhonjiswa khona. Bese uchofoza inkinobho ejwayelekile kusuka ezindleleni zangaphambilini. "Faka umsebenzi".



4. Iwindi elisebenzayo Amakhosi omsebenzi. Iya kusigaba "Isibalo" futhi phakathi kohlu lwabaqhubi, khetha igama lapho I-MOPRED. Emva kwalokho, chofoza inkinobho "Kulungile".



5. Iwindi lempikiswano yokusebenza iqala. MEPRED. Njengoba ungabona, inensimu eyodwa kuphela - "Uhlu". Faka ikheli le-matrix yokuqala eguquliwe kule nsimu. Ukuze wenze lokhu, setha isikhangiso endle, bese ukhetha ibanga le-matrix. Emva kwalokho, chofoza inkinobho "Kulungile". Lo msebenzi ubonisa umphumela esitokisini esisodwa, kunokuba uhlalwe, ngakho-ke ukuthola ukuthola, akudingeki ukuthi usebenzise ukucindezela inhlanganisela eyinhloko Ctrl + Shift + Faka.



6. Umsebenzi ubala umphumela futhi uwubonise kuseli elanduliwe. Njengoba sibona, kithi, i-determinant is -740, okungukuthi, akulingani ne-zero esithandela.



7. Ngokufanayo, sibala izinqumo zamanye amathebula amathathu.



8. Esigabeni sokugcina, sibala ukuthi isisindo somthamo esiyinhloko sinquma yini. Inqubo yonke i-algorithm efanayo. Njengoba sibona, i-determinant yetafula eliyisisekelo futhi aliyona i-nonzero, okusho ukuthi i-matrix ibhekwa njenge-nondegenerate, okungukuthi, isistimu ye-equations inezixazululo.



9. Manje sekuyisikhathi sokuthola izimpande ze-equation. Umsuka we-equation uzolingana nesilinganiso se-determinant ye-matrix eguquguqukayo ehambelana nesilinganiso setafula eliyinhloko. Ngakho, ukuhlukanisa zonke izici ezine zamatrices ashintshiwe ngenombolo -148okuyinto okuyisisekelo setafula langempela, sithola izimpande ezine. Njengoba ubona, zilingana namanani 5, 14, 8 futhi 15. Ngakho-ke, zifana ncamashi nezimpande esizitholile besebenzisa i-matrix inverse ku indlela 1okufakazela ukufaneleka kwesisombululo sesistimu ye-equations.

Indlela 4: Indlela kaGauss

Uhlelo lwe-equations lungasombululwa ngokusebenzisa indlela yeGauss. Isibonelo, masihambe ngesistimu elula yokulinganisa kusuka emithathu engaziwa:


14x1+2x2+8x3=110
7x1-3x2+5x3=32
5x1+x2-2x3=17

1. Siphinda sibhala phansi njalo ama coefficients etafuleni. Akanye namalungu wamahhala ngemuva kwesibonakaliso kufana - etafuleni B. Kodwa manje sizoletha amatafula amabili ndawonye, ​​ngoba sizodinga lokhu ukuze sisebenze ngokuqhubekayo. Isimo esibalulekile wukuthi esitokisini sokuqala se-matrix A Inani alilona elingu-zero. Ngaphandle kwalokho, lungisa kabusha imigqa.



2. Kopisha irowu lokuqala lamatriki amabili axhunyiwe emgqeni ngezansi (ngokucacile, ungakwazi ukweqa umugqa owodwa). Esitokisini sokuqala, esitholakala emgqeni ngisho nangaphansi kweyaphambilini, faka ifomula elandelayo:

   = B8: E8- $ B $ 7: $ E $ 7 * (B8 / $ B $ 7)

   Uma uhlele ama-matrixes ngokuhlukile, amakheli wamaseli wefomula uzoba nencazelo ehlukile, kodwa uzokwazi ukubala ngokuwaqhathanisa namafomula nezithombe ezinikezwe lapha.

   Ngemuva kokuthi ifomula ingenwe, khetha wonke umugqa wamaseli bese ucindezela inhlanganisela yekhiye Ctrl + Shift + Faka. Ifomula yefomu izosetshenziselwa umugqa futhi izogcwaliswa ngamanani. Ngakho-ke, sisusa emgqeni wesibili weyokuqala, siyanwetshwa yi-coefficients yokuqala yezinkulumo ezimbili zokuqala zesistimu.



3. Ngemva kwalokho, kopisha uchungechunge olulandelayo bese ulinamathisela emgqeni ngezansi.



4. Khetha imigqa emibili yokuqala ngemuva komugqa olahlekile. Sicindezela inkinobho "Kopisha"okuyinto itholakala kwi Ribbon kuthebhu "Ikhaya".



5. Sidlula umugqa ngemuva kokungena kokugcina kushidi. Khetha iseli lokuqala emgqeni olandelayo. Chofoza inkinobho yesokudla yegundane. Emenyu yemenyu evulwe, thuthela isikhombisi into "Namathisela Okukhethekile". Uma usebenzisa olunye uhlu, khetha isikhundla "Amanani".



6. Emgqeni olandelayo, faka ifomula yamalungu. Ikhupha kusukela emgqeni wesithathu weqembu ledatha langaphambilini umugqa wesibili ukhuliswa isilinganiso se-coefficient yesibili emgqeni wesithathu nowesibili. Esikhathini sethu, ifomula izoba kanje:

   = B13: E13- $ B $ 12: $ E $ 12 * (C13 / $ C $ 12)

   Ngemva kokufaka ifomula, khetha yonke uchungechunge bese usebenzisa ukhiye wezinqamuleli Ctrl + Shift + Faka.



7. Manje kuyadingeka ukukhipha okuphambene nokugijima ngokuya ngendlela yeGauss. Yeqa imigqa emithathu kusukela kokungena kokugcina. Emgqeni wesine, faka ifomula elandelayo:

   = B17: E17 / D17

   Ngakho-ke, sihlukanisa umugqa wokugcina obalwe nguwe ku-coefficient yayo yesithathu. Emva kokuthayipha ifomula, khetha yonke umugqa bese ucindezela inhlanganisela yekhiye Ctrl + Shift + Faka.



8. Siphakamisa umugqa up bese ufaka kuwo ifomula elandelayo:

   = (B16: E16-B21: E21 * D16) / C16

   Sicindezela inhlanganisela evamile yezihluthulelo zokusebenzisa ifomula yamalungu.



9. Siphakamisa enye inamba ngaphezulu. Kulokho singenisa ifomula elandelayo yefomu elandelayo:

   = (B15: E15-B20: E20 * C15-B21: E21 * D15) / B15

   Futhi, khetha yonke umugqa bese usebenzisa isinqamuleli Ctrl + Shift + Faka.



10. Manje sibheka izinombolo ezavela kukholomu yokugcina yesigcawu sokugcina semigqa, sibalwe ngathi ngaphambili. Yilezi izinombolo (4, 7 futhi 5) kuyoba izimpande zalesi simiso sokulingana. Ungahlola lokhu ngokufaka endaweni yazo ngamagugu. X1, X2 futhi X3 ezinkulumweni.

Njengoba ubona, ku-Excel, isistimu ye-equations ingaxazululwa ngezindlela eziningi, ngayinye yayo inezinzuzo zayo kanye nezinsalela. Kodwa zonke lezi zindlela zingahlukaniswa ngamaqembu amakhulu amabili: i-matrix futhi isebenzisa ithuluzi lokukhetha iparameter. Kwezinye izimo, izindlela zokwenza izibalo akuzona ngaso sonke isikhathi ezifanele ukuxazulula inkinga. Ngokuyinhloko, uma isinqumo se-matrix siyi-zero. Kwezinye izimo, umsebenzisi ukhululekile ukunquma ukuthi iyiphi inketho ayibheka yona elula kakhulu.