Momwe mungathere dongosolo labwino kwambiri

Kutha kuthetsa dongosolo la madongosolo nthawi zambiri amatha kupindula osati kuphunzira, komanso muzochita. Nthawi yomweyo, osagwiritsa ntchito PC aliyense amene amadziwa kuti ku ukapolo kumakhala ndi mitundu yake ya mayankho a ma equation. Tiyeni tiwone momwe kugwiritsa ntchito malangizo a purosedssit kukachita ntchito imeneyi m'njira zosiyanasiyana.

Zosankha za mayankho

Kufanana kulikonse kumatha kusinthidwa kokha pokhapokha mizu yake ipezeka. Kupambana, pali njira zingapo zosaka mizu. Tiyeni tiwone chilichonse cha izo.

Njira 1: Njira ya Matrix

Njira yofala kwambiri yothetsera dongosolo la Zida Zofanana ndi Exarl ndi kugwiritsa ntchito njira ya matrix. Imakhala ikupanga matrix a matrix a coe, kenako ndikupanga matrix obwerera. Tiyeni tiyesetse kugwiritsa ntchito njirayi kuti ithetse dongosolo lotsatirali:

14x1 + 2x2 + 8x4 = 218

7x1-3x2 + 5x3 + 12x4 = 213

5x1 + x2-2x3 + 4x4 = 83

6x1 + 2x2 + x3-3x4 = 21

1. Lembani manambala a matrix omwe ali ndi manambala a equation. Manambalawa amayenera kukhala motsatizana, poganizira momwe muzu uliwonse umatchulirana. Ngati imodzi mwa mizu ilibe mawu ena, pakadali pano kulumikizana kumawonedwa kuti ndi zero. Ngati kulumikizana sikunayikidwe mu equation, koma muzu wolinganizidwa, kumakhulupirira kuti kulumikizana ndi 1. Kutanthauzira ndi tebulo lotsatira ngati verctor A.



2. Lembani zinthu zomwe zikakhala chizindikiro "wofanana". Tinatanthauza dzina lawo ngati Varctor B.



3. Tsopano, kuti mupeze mizu ya equation, choyamba pa zonse, tiyenera kupeza matrix akuyandikira. Mwamwayi, excel ili ndi wothandizira wapadera, womwe umapangidwa kuti uthetse ntchitoyi. Amatchedwa mkuwa. Ili ndi syntax yosavuta:

   = Mebu (mndandanda)

   Mfundo "gulu", makamaka, adilesi ya tebulo la dameji.

   Chifukwa chake, timayika dera la ma cell opanda kanthu pa pepalalo, lomwe kukula kwake ndilofanana ndi mitundu yoyambirira ya matrix yoyambayo. Dinani batani "Ikani ntchito", yomwe ili pafupi ndi mawonekedwe.



4. Makina a Wizard amathamanga. Pitani ku gulu la "masamu". M'ndandanda wa "mkuwa" ukuwoneka kuti ukuwona mndandanda. Pambuyo papezeka, timatsindika ndikudina batani la "OK".



5. Zenera la masewerawa limayamba. Ndi gawo limodzi lokha pankhani ya mikangano - "gulu". Apa mukufunika kutchula adilesi ya tebulo lathu. Pazifukwa izi, yambitsani cholozera m'munda uno. Kenako pini kumanzere kumanzere ndikuwonetsa malo omwe matrix ali. Monga mukuwonera, zambiri zomwe zimagwirira ntchito zimalowetsedwa zokha pazenera. Ntchito imeneyi itatha, imakhala yodziwikiratu kuti mudina batani la "OK", koma simuyenera kufulumira. Chowonadi ndi chakuti kukanikiza batani ili ndilofanana ndi kugwiritsa ntchito lamulo la Enter. Koma mukamagwira ntchito ndi array atamaliza kuyika formula, simuyenera kudina batani la Lowetsani, ndikukhazikitsa njira zazifupi za Ctrl + Shift. Chitani izi.



6. Chifukwa chake, zitatha izi, pulogalamuyi imawerengera komanso pazomwe zili m'dera lomwe tili ndi matrix, chotsekera.



7. Tsopano tifunika kuchulukitsa matrix pa Matrix B, yomwe imakhala ndi mfundo imodzi ya mfundo yomwe ili pambuyo pa chikwangwani "ofanana. Kuchulukitsa magome apakulimo, palinso ntchito yosiyana yotchedwa MRM. Wogwiritsa ntchitoyu ali ndi syntax:

   = Mayi (ARY1; Array2)

   Timatsindika pamlingo, malinga ndi maselo anayi. Kenako, yambaninso ntchito za ntchitozo podina chithunzi cha "phala ntchito".



8. Mu "masamu", amayendetsa wizard ya ntchito, amagawa dzina "Mumznom" ndikusindikiza batani la "Ok".



9. Windo la Masewera Linakonzedwa. Mumunda "chachikulu1" timayambitsa mgwirizano wa matrix athu osinthika. Pachifukwa ichi, ngati nthawi yotsiriza, timakhazikitsa chotchinga m'munda ndi batani lakumanzere, tikutsindika chotemberera tebulo lofananalo. Zochita zomwezo zimachitika kuti mupange gawo la "chachikulu2" Gawani mfundo za nambala B. Pambuyo pa zomwe zili pamwambapa zidachitika, osathamangira kukanikiza batani la "Ok" kapena Kiyi ya Enter, ndi lembani ctrl + yosasunthira + yolowera kulowa.



10. Pambuyo pa izi, mizu ya equation idzawonetsedwa m'ndende yodziperekayi: X1, X1, X2, X3 ndi X4. Adzapezeka nthawi zonse. Chifukwa chake, titha kunena kuti tidathetsa dongosolo lino. Kuti mutsimikizire kulondola kwa yankho, ndikokwanira kuloweza deta yofikira ku dongosolo loyambirira m'malo mwa mizu yofananira. Ngati kufananako kumalemekezedwa, izi zikutanthauza kuti dongosolo loyimiriridwa limathetsedwa molondola.

Phunziro: Kusintha matrix ku Excel

Njira 2: Kusankhidwa kwa magawo

Njira yachiwiri yodziwika yothetsera dongosolo la equation mu Exadel ndikugwiritsa ntchito njira yosankha. Chizindikiro cha njirayi ndikupeza kuchokera ku zosiyana. Ndiye kuti, kutengera zotsatira zake, timapanga mkangano wosadziwika. Tiyeni tigwiritse ntchito gawo lalikulu mwachitsanzo

3X ^ 2 + 4X-132 = 0

1. Tengani mtengo wa X ofanana ndi 0. Loondani mtengo wolingana ndi mtengo wa Mtengo wa F (X) pogwiritsa ntchito njira zotsatirazi:

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

   M'malo motanthauza tanthauzo la "x" Timalowetsa adilesi ya selo pomwe nambala 0 yomwe idatengedwa nafe ya x ili.



2. Pitani ku "deta" tabu. Tadina pa "kusanthula" Bwanji "." Batani ili limayikidwa pa tepi mu "kugwira ntchito ndi data" chida. Mndandanda wotsika wotsika umatseguka. Sankhani malo oti "kusankha kwa parameter ...".



3. Zenera losankha la parameter limayambitsidwa. Monga mukuwonera, imakhala ndi minda itatu. Mu "gawo la" gawo la selo, fotokozerani adilesi ya selo yomwe f (x) formula imapezeka, kuwerengeredwa ndi ife kale. Mu gawo la "mtengo", timalowa manambala "0". Mu "Njira Yosintha", fotokozerani adilesi ya selo yomwe x yamtengo wapatali yomwe yatengedwa ndi 0. Pambuyo pochita izi, dinani batani la "Ok".



4. Pambuyo pake, Excel imawerengera pogwiritsa ntchito chisankho. Izi zikunenedwa kuti afotokoze zenera. Iyenera kukanikizidwa pa batani la "OK".



5. Zotsatira za kuwerengetsa mizu ya equation kudzakhala mu cell yomwe tasankhidwa mu njira ya "Kusintha". Kwa ife, monga tikuwona, X idzakhala yolingana ndi 6.

Zotsatirazi zitha kufufuzidwanso ndi kuloweza mtengo uwu kukhala mawu osinthika m'malo mwa X mtengo.

Phunziro: Kusankhidwa kwa parament ku Excel

Njira 3: Njira ya Craver

Tsopano tiyeni tiyesetse kuthetsa dongosolo la englition ndi cramer. Mwachitsanzo, tengani dongosolo lomwelo lomwe linagwiritsidwa ntchito munjira 1:

14x1 + 2x2 + 8x4 = 218

7x1-3x2 + 5x3 + 12x4 = 213

5x1 + x2-2x3 + 4x4 = 83

6x1 + 2x2 + x3-3x4 = 21

1. Monga momwe munjira yoyamba, timapanga matrix kuchokera pazithunzi za ma equation ndi tebulo kuchokera pazomwe zimayimira chizindikirocho "chofanana."



2. Kenako, timapanga matebulo ena anayi. Iliyonse a iwo ndi buku la matrix a, pokhapokha ngati pali ena omwe ali ndi gome B. Tebulo loyamba ndi gawo loyamba, patebulo lachiwiri - lachiwiri, lachiwiri, ndiwiri.



3. Tsopano tikufunika kuwerengera zoyeserera pa matebulo onse awa. Dongosolo la equation lidzakhala ndi mayankho pokhapokha ngati opanga onse adzakhala ndi mtengo wina kupatula zero. Kuti muwerenge mtengo uwu pa Excel, pali ntchito yosiyana - yotulutsidwa. Syntax ya wothandizira uyu ali motere:

   = Opindika (mndandanda)

   Chifukwa chake, monga ntchito ya mkuwa, mkangano wokhawo umatchulidwa patebulo yomwe ikukonzedwa.

   Chifukwa chake, tikutsindika khungu lomwe kutsikira kwa matrix yoyamba ikhale yotulutsa. Kenako dinani batani la "Intern Act" patsamba lakale.



4. ZABWINO ZOPHUNZITSIRA BWINO. Timatembenukira ku gulu la "masamu" ndipo pakati pa mndandanda wa ogwiritsa ntchito "adayika dzina" lolomoka "pamenepo. Pambuyo pake, dinani batani la "OK".



5. Zenera la Mphaka Logundika limayamba. Monga mukuwonera, ili ndi gawo limodzi lokha - "gulu". Mu gawo ili, lowetsani adilesi ya matrix oyamba. Kuti muchite izi, khazikitsani chotengera m'munda, kenako sankhani matrix osiyanasiyana. Pambuyo pake, dinani batani la "OK". Ntchitoyi imawonetsa zotsatira chimodzi mu khungu limodzi, osati mndandanda, kotero kuti muwerengere, simuyenera kuyesa kupanga CTRL + Kusunthira Kwezani.



6. Ntchitoyo imawerengera zotsatira zake ndikuwonetsa mu khungu losankhidwa. Monga tikuwonera, monga taganizira za kukhala lofanana ndi -740, ndiye kuti, sizofanana ndi zero, zomwe zikugwirizana nafe.



7. Mofananamo, timawerengera za otsimikizika a matebulo ena atatu.



8. Pamapeto omaliza, imawerengedwa ndi kutsimikizika kwa matrix oyamba. Njirayi imachitika mogwirizana ndi algorithm yemweyo. Monga tikuwona, tebulo loyambirira limasiyananso ndi zero, zomwe zikutanthauza kuti matrix amawaganizira kuti kulibe, ndiye kuti, kachitidwe ka equation kuli ndi yankho.



9. Tsopano ndi nthawi yoti mupeze mizu ya equation. Muzu wa equation udzakhala wofanana ndi chiwerengero cha chotsimikizika cha matrix osinthidwa kukhala okhazikika patebulo lalikulu. Chifukwa chake, adagawanenso mosiyanasiyana kwa matrictforated matrictfic zosinthidwa kukhala nambala - yomwe ndi yotsimikizika ya tebulo loyambirira, timapeza mizu inayi. Monga tikuonera, ndi ofanana ndi zikhalidwe 5, 14, 8, 8, 8 mpaka 15. Chifukwa chake, motero amapezekanso ndi mizu yomwe tidapeza kuti ikugwiritsa ntchito matrix munjira ya equation dongosolo.

Njira 4: Njira ya Gauss

Kuthetsa dongosolo la equation kumathanso kugwiritsidwanso ntchito ndi njira ya Gauss. Mwachitsanzo, timatenga kachitidwe kakang'ono ka ziyeso zitatu:

14x1 + 2x2 + 8x3 = 110

7x1-3x2 + 5x3 = 32

5x1 + x2-2x3 = 17

1. Apanso, tengani ma coefficals mu tebulo a, ndipo mamembala aulere omwe ali ndi "chizindikiro" chofanana "- patebulo b. Koma nthawi ino lidzasonkhana matebulo onse, chifukwa chidzafunika kugwirira ntchito mtsogolo. Chofunikira ndichakuti mu khungu loyamba la Matrix mtengo wosiyana ndi zero. Mosakayikira, mizereyo iyenera kukonzedwanso.



2. Koperani chingwe choyambirira cha matric awiri olumikizidwa mu mzere pansipa (chifukwa chofananira mutha kudumpha mzere umodzi). Mu khungu loyamba, lomwe lili mu mzere ndilotsika kuposa kale, timayambitsa njira yotsatirayi:

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

   Ngati mwayika matric m'njira ina, ndiye ma adilesi a maselo a fomu yomwe mungakhale ndi phindu lina, koma mutha kuwerengera poyerekeza ndi mapangano ndi zithunzi zomwe zaperekedwa pano.

   Pambuyo pa formula atalowetsedwa, sonyezani za maselo onse ndikusindikiza Ctrl + Shift + ENTER EXT. Njira yothetsera fomula idzagwiritsidwa ntchito pamzere ndipo idzadzazidwa ndi mfundo. Chifukwa chake, tidatichotsa pamzere wachiwiri wazomwe zidanenedwa koyambirira ndi kuchuluka kwa ma coemoter oyamba a dongosololi.



3. Pambuyo potengera chingwe chomwe chimapangitsa kuti chizinga ndi kuyika mzere womwe uli pansipa.



4. Sankhani mizere iwiri yoyamba itatha. Dinani pa batani la "Copy", yomwe ili pa tepi mu tabu yakunyumba.



5. Tikudulira chingwe pambuyo polowera komaliza papepala. Sankhani selo yoyamba pamzere wotsatira. Dinani batani lamanja. Muzosankha zomwe zatsegula cholozera ku "gawo lapadera". M'ndandanda womwe watchulidwa pamwambapa, sankhani "mtengo".



6. Ku mzere wotsatira timayambitsa njira yatsamba. Zimapangitsa kuti zitheke kuza mzere wachitatu wa gulu lakale la data lachiwiri lochulukitsidwa ndi kuchuluka kwa chindachi chachiwiri ndi chachiwiri. M'malo mwathu, fomulayo idzakhala ndi mawonekedwe awa:

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

   Pambuyo polowa njirayi, timagawa gawo lonse ndikugwiritsa ntchito CTRL + Shift + kulowa m`tunga.



7. Tsopano muyenera kugwira ntchito yakumbuyo malinga ndi njira ya Gauss. Timadumpha mizere itatu kuchokera kulowera komaliza. Mu mzere wachinayi timayambitsa njira ya mndandanda:

   = B17: E17 / D17

   Chifukwa chake, timagawa chingwe chaposachedwa chaposachedwa ndi ife pa gawo lake lachitatu. Pambuyo pa fomu yaimira, tikuwonetsa mzere wonse ndikudina CTRL + Shift + Lowani kiyibodi.



8. Timadzuka zingwe ndikulowa mndandanda wotsatirawu momwemo:

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

   Tikudina mwachidule kuti tigwiritse ntchito njira ya Agera.



9. Kwezani mzere wina pamwamba. Mwa iye amadziwitsa mtundu wa mitundu yotsatirayi:

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

   Apanso, gawirani chingwe chonse ndikugwiritsa ntchito CTRL + Shift + ENTER EXT.



10. Tsopano tikuyang'ana manambala omwe adapezeka mumzere wotsiriza wa malo omaliza a mizere yomwe imawerengedwa nako kale. Ndi manambala (4, 7 ndi 5) omwe azikhala mizu ya dongosolo lino la equation. Mutha kuyang'ana izi, m'malo mwa X1, X2 ndi X3 mu mawu.

Monga tikuwonera, zochulukirapo, kachitidwe ka mapangidwe kungathetsedwe mwa njira zingapo, chilichonse chomwe chili ndi zabwino zake komanso zovuta zake. Koma njira zonsezi zitha kugawidwa m'magulu awiri: Matrix ndi kugwiritsa ntchito chida chosankha. Nthawi zina, njira za matrix sizoyenera nthawi zonse kuthetsa vutoli. Makamaka, pomwe zotsimikizika za matrix ndi zero. Potsalazo, wogwiritsa ntchito yekhayo amadikirira kuti aganize njira yomwe akuwaganizira moyenera.