Kujambula mu Writing OpenOffice. Tsamba Loyambira Yoyambira

Kukwanitsa kuthetsa machitidwe a equations kungakhale kopindulitsa osati kusukulu kokha, komanso m'zochita. Pa nthawi yomweyi, sikuti aliyense wogwiritsa ntchito PC amadziwa kuti Excel ili ndi njira zake zothetsera ziwerengero zofanana. Tiyeni tione momwe kugwiritsira ntchito bukhuli lopangira pulogalamuyi kukwaniritsa ntchitoyi m'njira zosiyanasiyana.

Zothetsera

Ma equation aliwonse akhoza kuthandizidwa kuthetsedwa kokha pamene mizu yake imapezeka. Mu Excel, pali njira zingapo zopezera mizu. Tiyeni tiyang'ane pa aliyense wa iwo.

Njira 1: Matrix Method

Njira yowonjezereka yothetsera kayendedwe kazithunzi zofanana ndi zida za Excel ndi kugwiritsa ntchito njira yamakono. Zimapanganso kumanga matrix kuchokera kumagulu a mawu, ndiyeno popanga matrix. Tiyeni tiyesere kugwiritsa ntchito njira iyi kuthetsa dongosolo lotsatizana lazigawo:


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

1. Timadzaza matrix ndi manambala omwe ali coefficients of equation. Ziwerengerozi ziyenera kukonzedweratu motsatira ndondomekoyi, poganizira malo omwe muzuwo umayendera. Ngati mukulongosola kwina, imodzi mwa mizu ikusowa, ndiye pakaliyi coefficient ikuyesedwa ndi ofanana ndi zero. Ngati coefficient sichiwonetsedwa mu equation, koma mizu yofananayo ilipo, zikuyesa kuti coefficient ndi ofanana 1. Tchulani tebulo lomwe liri ngati vector A.



2. Mosiyana, timalembera makhalidwe pambuyo pa chizindikiro chofanana. Awatchule mwa dzina lawo monga vector B.



3. Tsopano, kuti tipeze mizu ya equation, choyamba, tifunika kupeza matrix, kutsogolo kwa zomwe zilipo. Mwamwayi, ku Excel pali wapadera opangidwa kuti athetse vutoli. Icho chimatchedwa MOBR. Lili ndi mawu omveka bwino:

   = MBR (gulu)

   Kutsutsana "Mzere" - izi ndizo, adiresi ya gome la gwero.

   Kotero, ife timasankha pa pepala gawo la maselo opanda kanthu, omwe ali ofanana mofanana ndi kukula kwa chiyero choyambirira. Dinani pa batani "Ikani ntchito"ili pafupi ndi bar.



4. Kuthamanga Oyang'anira ntchito. Pitani ku gawo "Masamu". Mndandanda ife tikuyang'anira dzina "MOBR". Pambuyo popezeka, sankhani ndipo dinani pa batani. "Chabwino".



5. Ntchito yotsutsana zenera ikuyamba. MOBR. Lili ndi munda umodzi wokha mwa chiwerengero cha zifukwa - "Mzere". Pano muyenera kufotokoza adiresi ya tebulo lathu. Kwa zolinga izi, yikani cholozera mmunda uno. Kenako timagwiritsa ntchito batani lamanzere ndikusankha malo omwe ali pamapepala omwe amapezeka. Monga momwe mukuonera, deta pamakonzedwe a malo amalowa mwadongosolo pazenera. Pambuyo pa ntchitoyi yatsirizidwa, zoonekeratu zikanakhala kuti dinani batani. "Chabwino"koma musachedwe. Chowonadi ndikuti kudindikiza batani iyi ndilofanana ndi kugwiritsa ntchito lamulo Lowani. Koma mukamagwira ntchito pamodzi ndi ndondomekoyo musanamalize batani. Lowanindi kutulutsa makina achitsulo Ctrl + Shift + Lowani. Chitani opaleshoniyi.



6. Kotero, patatha izi, pulogalamuyi imapanga ziwerengero ndi zotsatira za malo omwe tinasankhidwa kale omwe tili ndi chiwerengero cha matrix.



7. Tsopano tifunikira kuchulukitsa chivundikiro choyendetsa ndi matrix. Bzomwe zili ndi ndondomeko imodzi yomwe ilipo pambuyo pa chizindikiro zofanana mu mawu. Pakuti kuwonjezeka kwa matebulo mu Excel kumakhala ndi ntchito yosiyana, yomwe imatchedwa Mayi. Mawu awa ali ndi zizindikiro zotsatirazi:

   = MUMNOGUE (Array1; Array2)

   Sankhani zamtunduwu, m'mabuku athu omwe ali ndi maselo anayi. Kenaka muthamange kachiwiri Mlaliki Wachipangizopotsegula chithunzicho "Ikani ntchito".



8. M'gululi "Masamu"akuthamanga Oyang'anira ntchitosankhani dzina "MUMNOZH" ndipo dinani pa batani "Chabwino".



9. Ntchito yotsutsana zenera ikusegulidwa. Mayi. Kumunda "Massive1" lowetsani makonzedwe a masanjidwe athu ozungulira. Kuti muchite izi, monga nthawi yomaliza, yikani mtolo mmunda ndi batani lamanzere lomwe likugwiritsidwa ntchito, sankhani tebulo lolingana ndi ndondomeko. Zomwezo zimachitidwa kuti apange mgwirizano mmunda "Massiv2", pokhapokha nthawi ino timasankha mfundo zamtengo wapatali. B. Pambuyo pazomwe zatchulidwa pamwambapa, sitimangothamanga pakani "Chabwino" kapena fungulo Lowani, ndipo lembani mgwirizano Ctrl + Shift + Lowani.



10. Zitatha izi, mizu ya equation ikuwoneka mu selo losankhidwa kale: X1, X2, X3 ndi X4. Iwo adzakonzedwa mndandanda. Choncho, tinganene kuti tathetsa dongosolo lino. Pofuna kutsimikizira kuti yankho lake ndi lolondola, ndikwanira kulowetsa mayankho omwe wapatsidwa muyambidwe yoyambirira m'malo mwa mizu yofanana. Ngati kulumikizana kumasungidwa, izi zikutanthauza kuti dongosolo la equations likufotokozedwa bwino.

Phunziro: Excel Kusintha Matrix

Njira 2: kusankha magawo

Njira yodziwika yachiwiri yothetsera kayendedwe kabwino ka Excel ndiyo kugwiritsa ntchito njira yosankha. Chofunika cha njira iyi ndi kufufuza zosiyana. Izi ndizo, zokhudzana ndi zotsatira zodziwika, timayang'ana kutsutsana kosadziwika. Tiyeni tigwiritse ntchito quadratic equation mwachitsanzo.

3x ^ 2 + 4x-132 = 0

1. Landirani mtengo x zofanana 0. Yerengani mtengo wofanana nawo f (x)mwa kugwiritsa ntchito njira yotsatirayi:

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

   Mmalo mwa mtengo "X" alowetsani adilesi ya selo kumene chiwerengerocho chili 0watengedwa ndi ife x.



2. Pitani ku tabu "Deta". Timakanikiza batani "Kufufuza" bwanji ngati. Bululi likuyikidwa pa kaboni mu bokosi lazamasamba. "Kugwira ntchito ndi deta". Mndandanda wotsika. Sankhani malo mmenemo "Kusankhidwa kwapakati ...".



3. Zenera zosankha zosankha zimayambira. Monga mukuonera, ilo liri ndi minda itatu. Kumunda "Sakani mu selo" tchulani adiresi ya selo imene machitidwewo ali f (x)tinawerengedwa ndi ife kanthawi kochepa. Kumunda "Phindu" lowetsani nambalayi "0". Kumunda "Kusintha Makhalidwe" tchulani adiresi ya selo komwe mtengo ulipo xpoyamba tinasankhidwa ndi ife 0. Mutatha kuchita izi, dinani pa batani "Chabwino".



4. Pambuyo pake, Excel idzachita chiwerengero pogwiritsa ntchito njira yosankha. Izi zidziwitsa zowonekera zowonekera. Iyenera kudina pa batani "Chabwino".



5. Zotsatira za kuwerengera kwa muzu wa equation zidzakhala mu selo lomwe tapatsidwa kumunda "Kusintha Makhalidwe". Kwa ife, monga ife tikuwonera x adzakhala ofanana ndi 6.

Chotsatirachi chikhoza kuyang'ananso mwa kusinthitsa phindu ili muzitsulo zosinthidwa mmalo mwa mtengo x.

Phunziro: Chisankho cha Excel

Njira 3: Njira ya Cramer

Tsopano ife tiyesera kuthetsa dongosolo la equations ndi njira ya Kramer. Mwachitsanzo, tiyeni titenge dongosolo lomwelo lomwe linagwiritsidwa ntchito Njira 1:


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

1. Monga mwa njira yoyamba, timapanga matrix A kuchokera ku coefficients ya equations ndi tebulo B za makhalidwe omwe amatsatira chizindikiro zofanana.



2. Komanso tikupanga matebulo ena anayi. Chilichonse mwazo ndizojambula. A, makope awa okha ali ndi mzere umodzi m'malo mwa tebulo B. Mu tebulo yoyamba ndilo ndime yoyamba, mu tebulo yachiwiri ili yachiwiri, ndi zina zotero.



3. Tsopano tifunikira kuwerengera zosankha pa matebulo onsewa. Mchitidwe wa equations udzakhala ndi njira zothetsera pokhapokha ngati zizindikiro zonse zili ndi mtengo wina osati zero. Kuwerengera mtengo umenewu ku Excel kachiwiri pali ntchito yosiyana - MEPRED. Chidule cha mawu awa ndi awa:

   = MEPRED (gulu)

   Motero, monga ntchito MOBR, kukangana kokha ndikokutchulidwa kwa tebulo ikugwiritsidwa ntchito.

   Choncho, sankhani selo limene lingaliro loyamba la masanjidwe lidzawonetsedwa. Kenaka dinani pa batani omwe mumawadziwa kale. "Ikani ntchito".



4. Yatsegula zenera Oyang'anira ntchito. Pitani ku gawo "Masamu" ndipo pakati pa mndandanda wa ogwira ntchito, sankhani dzina pamenepo YAM'MBUYO. Pambuyo pake, dinani pa batani "Chabwino".



5. Ntchito yotsutsana zenera ikuyamba. MEPRED. Monga mukuonera, ili ndi munda umodzi - "Mzere". Lowetsani adiresi ya matrix yoyamba yosinthidwa kupita kumunda uno. Kuti muchite izi, yikani mtolo mmunda, ndiyeno musankhe mtundu wamatayi. Pambuyo pake, dinani pa batani "Chabwino". Ntchitoyi ikuwonetsa zotsatira mu selo limodzi, osati mzere, kotero kuti mupeze chiwerengero, simukusowa kugwiritsa ntchito makina osakaniza Ctrl + Shift + Lowani.



6. Ntchitoyi imatengera zotsatirazo ndipo imawonetsera mu selo yoyamba yosankhidwa. Monga tikuonera, kwa ife, determinant ndi -740, ndiko kuti, silifanana ndi zero zomwe zimatiyenereza.



7. Mofananamo, ife timawerengetsera ziganizo pa matebulo ena atatu.



8. Pamapeto omaliza, timawerengera chiwerengero choyambirira cha matrix. Ndondomekoyi ndi njira imodzimodziyo. Monga momwe tikuonera, chiwerengero cha tebulo lapamwamba ndichinanso, chomwe chikutanthauza kuti chiwerengero cha masanjidwe chimaonedwa ngati chitsimikizo, ndiko kuti, dongosolo la equation liri ndi zothetsera.



9. Tsopano ndi nthawi yoti mupeze mizu ya equation. Muzu wa equation udzakhala wofanana ndi chiŵerengero cha chidziwitso cha matrix osinthidwa ofanana ndi tebulo lalikulu. Choncho, kugawanitsa zigawo zonse zinayi za matrices osinthidwa ndi nambala -148chomwe chiri choyambirira cha tebulo lapachiyambi, timapeza mizu inayi. Monga mukuonera, iwo ali ofanana ndi makhalidwe 5, 14, 8 ndi 15. Kotero, iwo ali ofanana chimodzimodzi ndi mizu yomwe ife tinapeza pogwiritsa ntchito matrix mkati njira 1zomwe zimatsimikizira kulondola kwa njira yothetsera migwirizano.

Njira 4: Gauss Method

Mchitidwe wa equations ungathetsedwenso mwa kugwiritsa ntchito njira ya Gauss. Mwachitsanzo, tiyeni titenge njira yosavuta yogawa kuchokera pa zitatu zosadziwika:


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

1. Apanso timalemba coefficients mu tebulo. Andi mamembala aufulu pambuyo pa chizindikiro zofanana - ku tebulo B. Koma nthawi ino tidzabweretsa magome awiri palimodzi, chifukwa tidzasowa izi kuti tigwire ntchito. Chikhalidwe chofunika ndi chakuti mu selo yoyamba ya matrix A mtengo unali wosakhala zero. Apo ayi, yongolani mizere.



2. Lembani mzere woyamba wa matrices awiri okhudzana nawo mu mzere uli pansipa (kwachidule, mukhoza kudutsa mzera umodzi). Mu selo yoyamba, yomwe ili mu mndandanda ngakhale mocheperapo kuposa yapitayo, lowetsani ndondomeko yotsatirayi:

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

   Ngati munakonza matrixes mosiyana, ndiye kuti maadiresi a maselo omwe mumakhala nawo amatha kutanthauzira mosiyana, koma mudzatha kuwawerengera, powayerekeza ndi mafomu ndi zithunzi zomwe zafotokozedwa pano.

   Pambuyo polowera ndondomekoyi, sankhani mzere wonse wa maselo ndikusindikiza kuphatikiza Ctrl + Shift + Lowani. Ndondomekoyi idzagwiritsidwa ntchito pamzerewu ndipo idzadzaza ndi mfundo. Kotero, ife tinachotsamo kuchokera mzere wachiwiri wa woyamba, kuchulukitsidwa ndi chiŵerengero cha coefficients yoyamba ya mawu awiri oyambirira a dongosolo.



3. Pambuyo pake, lembani chingwe chotsatira ndikuchiyika mumzere uli pansipa.



4. Sankhani mizere iwiri yoyamba pambuyo pa mzere wosowa. Timakanikiza batani "Kopani"yomwe ili pa leboni mu tabu "Kunyumba".



5. Tikudumpha mzere pambuyo polowera pa pepala. Sankhani selo yoyamba mu mzere wotsatira. Dinani botani lamanja la mouse. Mu menyu yotseguka, yendetsani cholozera ku chinthucho "Sakani Mwapadera". Mu mndandanda wowonjezera, sankhani malo "Makhalidwe".



6. Mu mzere wotsatira, lowetsani ndondomeko yambiri. Icho chimachotsa kuchoka pa mzere wachitatu wa gulu ladatha la deta mzere wachiwiri wochulukitsidwa ndi chiŵerengero cha yachiwiri coefficient chachitatu ndi mzere wachiwiri. Kwa ife, dongosololi lidzakhala motere:

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

   Pambuyo polowera ndondomekoyi, sankhani mndandanda wonse ndikugwiritsa ntchito njira yochezera Ctrl + Shift + Lowani.



7. Tsopano ndikofunikira kuti zitsatire zosiyana molingana ndi njira ya Gauss. Dulani mizere itatu kuchokera kumapeto kotsiriza. Mu mzere wachinayi, lowetsani ndondomekoyi:

   = B17: E17 / D17

   Potero, timagawira mzere wotsiriza womwe timayesedwa ndi ife mu coefficient yake yachitatu. Pambuyo pakulemba fomuyi, sankhani mzere wonse ndikusindikiza kuphatikiza Ctrl + Shift + Lowani.



8. Timakweza mzere ndikulowa mmenemo njira yotsatirayi:

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

   Timagwiritsa ntchito mafungulo omwe amagwiritsidwa ntchito pogwiritsa ntchito ndondomekoyi.



9. Ife tikukwera mmwamba mzere umodzi pamwambapa. Mmenemo timalowa njira yotsatirayi:

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

   Apanso, sankhani mzere wonse ndikugwiritsa ntchito njirayo Ctrl + Shift + Lowani.



10. Tsopano tikuyang'ana chiwerengero chomwe chinapezeka mu gawo lomalizira la mzere wa mizere, yomwe tinayiwerengera kale. Ndi nambala izi (4, 7 ndi 5) adzakhala mizu ya kayendedwe ka machitidwewa. Mukhoza kufufuza izi mwa kuziika m'malo mwazofunika. X1, X2 ndi X3 mu mawu.

Monga mukuonera, mu Excel, dongosolo la equations lingathetsedwe m'njira zingapo, zomwe zili ndi ubwino wake ndi zovuta zake. Koma njira zonsezi zingagawidwe m'magulu akulu awiri: matrix ndikugwiritsa ntchito chida chosankha. Nthawi zina, njira zamakono sizili zoyenera kuthetsera vuto. Makamaka, pamene determinant ya matrix ndi zero. Nthawi zina, wogwiritsa ntchitoyo ndi ufulu kusankha chomwe amachiona kuti n'chophweka kwambiri.