Kutha kuthetsa machitidwe a equation nthawi zambiri kumatha kukhala kothandiza osati pophunzira, komanso machitidwe. Nthawi yomweyo, sikuti wogwiritsa ntchito PC aliyense amadziwa kuti Excel ali ndi njira zake zothetsera ma mzere mzere. Tiyeni tiwone momwe mungagwiritsire ntchito pulogalamu iyi ya purosesa ya tebulo kuti mukwaniritse ntchitoyi m'njira zosiyanasiyana.
Zisankho
Chiyeso chilichonse chimatha kusemedwa pokhapokha mizu yake ipezeka. Excel ali ndi zosankha zingapo zopezera mizu. Tiyeni tiwone aliyense wa iwo.
Njira 1: njira ya matrix
Njira yofala kwambiri yothetsera dongosolo lama equation okhala ndi zida za Excel ndikugwiritsa ntchito njira ya matrix. Amakhala ndikupanga matrix of expression coefficients, kenako ndikupanga matrix osinthika. Tiyeni tiyese kugwiritsa ntchito njirayi kuthetsa njira zotsatirazi:
14x1+2x2+8x4=218
7x1-3x2+5x3+12x4=213
5x1+x2-2x3+4x4=83
6x1+2x2+x3-3x4=21
- Timadzaza matrix ndi manambala, omwe ndi ma coefficients a equation. Manambalawa ayenera kuikidwa motsatira dongosolo, kukumbukira malo omwe muzu uliwonse umagwirizana. Ngati m'mawu amodzi umodzi mwa mizu mulibe, ndiye kuti pamenepa zonsezo zimawoneka kuti zofanana ndi zero. Ngati cholingacho sichikuwonetsedwa mu equation, koma pali muzu wolingana, ndiye kuti mgwirizowo ndi 1. Gwiranani patebulo lomwe lotsatira ngati vekitala A.
- Payokha, lembani zofunikira pambuyo pa chizindikiro chofanana. Apatseni dzina lawo wamba, ngati vekitala B.
- Tsopano, kuti tipeze mizu ya equation, choyambirira, tiyenera kupeza chosiyana cha chomwe chilipo. Mwamwayi, Excel ili ndi wothandizira wapadera yemwe adapangidwa kuti athetse vutoli. Amayitanidwa MOBR. Ili ndi syntax yosavuta
= MOBR (gulu)Kukangana Menya - Uwu ndiye, adilesi ya gwero la magwero.
Chifukwa chake, timasankha pa pepalalo gawo la maselo opanda kanthu, omwe ali ofanana kukula ndi mtundu wa masanjidwe oyambira. Dinani batani "Ikani ntchito"ili pafupi ndi mzere wa fomula.
- Kuyambira Ogwira Ntchito. Pitani ku gulu "Masamu". Pamndandanda womwe umawonekera, yang'anani dzinalo MOBR. Akapezeka, sankhani ndikudina batani "Zabwino".
- Tsamba la mkangano wa ntchito likuyamba MOBR. Ili ndi gawo limodzi lokha pamipikisano - Menya. Apa muyenera kufotokoza adilesi yathu tebulo. Pazifukwa izi, ikani cholozera m'munda uno. Kenako timagwira batani lakumanzere ndikusankha zomwe zili patsamba lomwe matrix ili. Monga mukuwonera, zambiri pazogwirizanitsa za masanjidwe zimangokhazikitsidwa pazenera la zenera. Ntchito iyi ikamalizidwa, chodziwikiratu kwambiri ndikadina batani "Zabwino"koma osathamanga. Chowonadi ndi chakuti kuwonekera pa batani ili ndikofanana ndi kugwiritsa ntchito lamulo Lowani. Koma mukamagwira ntchito ndi magulu atatsiriza mawonekedwe a formula, musadina batani Lowani, ndikupanga njira zazifupi Ctrl + Shift + Lowani. Chitani izi.
- Chifukwa chake, izi zitatha, pulogalamuyi imachita kuwerengera ndipo, potulutsa zomwe zidasankhidwa kale, tili ndi matrix mosiyana ndi omwe tapatsidwa.
- Tsopano tifunikira kuchulukitsa matrix osinthika ndi matrix B, yomwe imakhala ndi mzere umodzi wamakhalidwe womwe uli pambuyo pa chikwangwani zofanana m'mawu. Kuchulukitsa matebulo ku Excel palinso ntchito ina yotchedwa MLUNGU. Mawu awa ali ndi syntax otsatirawa:
= Zambiri (Array1; Array2)Timasankha osiyanasiyana, m'malo mwathu, okhala ndi maselo anayi. Chotsatira, thamangani kachiwiri Fotokozerani Wizardmwa kuwonekera "Ikani ntchito".
- Gulu "Masamu"adakhazikitsa Ogwira Ntchito, sankhani dzinalo MUMNOZH ndipo dinani batani "Zabwino".
- Tsamba la mkangano wa ntchito limayambitsa. MLUNGU. M'munda "Pantan1" lowetsani zolumikizana ndi matrix athu osokoneza. Kuti muchite izi, monga nthawi yotsiriza, ikani cholozera m'munda ndipo batani lakumanzere likakanikizidwa sankhani tebulo lolingana ndi chowunikira. Timachitanso zofananazo kuti tithandizire kulimbikitsa magulu m'munda Array2, pokhapokha asankhe mfundo za mzere B. Zitachitika izi pamwambapa, sitikhala ofulumira kukanikiza batani "Zabwino" kapena kiyi Lowani, ndikulemba kuphatikiza kiyi Ctrl + Shift + Lowani.
- Pambuyo pa izi, mizu ya equation imawonetsedwa mu khungu lomwe lidasankhidwa kale: X1, X2, X3 ndi X4. Akonzedwa mndandanda. Chifukwa chake, titha kunena kuti tathetsa dongosolo lino. Kuti muwonetsetse kulondola kwa yankho, ndikukwanira kuyimilira mayankho anu mu dongosolo loyambirira lamalo m'malo mizu yolingana. Ngati kufanana kumawonedwa, ndiye kuti izi zikutanthauza kuti dongosolo lomwe limaperekedwa limasinthidwa molondola.
Phunziro: Matrix osokoneza mu Excel
Njira 2: kusankha magawo
Njira yachiwiri yodziwika yothetsera dongosolo la ma equation ku Excel ikugwiritsa ntchito njira yosankhira magawo. Chinsinsi cha njirayi ndikufufuza kuchokera kwina. Ndiye kuti, potengera zotsatira zodziwika, timafunafuna mkangano wosadziwika. Tiyeni tigwiritse ntchito equation ya quadratic monga chitsanzo
3x ^ 2 + 4x-132 = 0
- Landirani mtengo x ofanana 0. Timawerengera mtengo wolingana nawo f (x)kutsatira njira zotsatirazi:
= 3 * x ^ 2 + 4 * x-132M'malo mopindulitsa "X" sinthani adilesi ya foni komwe nambala ili 0otitengera x.
- Pitani ku tabu "Zambiri". Dinani batani "Bwanji ngati kusanthula". Izi batani limapezeka pa riboni m'bokosi la chida. "Gwirani ntchito ndi deta". Mndandanda wotsika pansi umatseguka. Sankhani malo mmenemu "Kusankhidwa kwamalire ...".
- Zenera losankha chizindikiro liyamba. Monga mukuwonera, ili ndi magawo atatu. M'munda Khalani mu cell fotokozerani adilesi yomwe foniyo ili f (x)kuwerengetsa ndi ife kale. M'munda "Mtengo" lowetsani nambala "0". M'munda "Kusintha Mfundo" fotokozerani adilesi ya foni momwe mtengo udakhalira xzomwe zidalandilidwa kale ndi ife 0. Mukamaliza izi, dinani batani "Zabwino".
- Pambuyo pake, Excel adzachita kuwerengera posankha gawo. Izi zidzanenedwa ndi zenera lowonekera. Mmenemo, dinani batani "Zabwino".
- Zotsatira zakuwerengera muzu wa equation zidzakhala mu cell yomwe tidayikiratu kumunda "Kusintha Mfundo". M'malo mwathu, monga tikuonera, x akhale ofanana 6.
Zotsatira zathu zitha kuyang'anidwanso poika mtengo m'malo mawuwo kuti uwonongedwe m'malo mwa phindu x.
Phunziro: Kusankhidwa kwa paramu ku Excel
Njira 3: Njira Za Cramer
Tsopano tiyeni tiyesetse kukonza dongosolo la ma equation pogwiritsa ntchito njira ya Cramer. Mwachitsanzo, tengani dongosolo lomweli lomwe limagwiritsidwa ntchito Njira 1:
14x1+2x2+8x4=218
7x1-3x2+5x3+12x4=213
5x1+x2-2x3+4x4=83
6x1+2x2+x3-3x4=21
- Monga momwe timafotokozera njira yoyamba, timayala matrix A kuchokera ku coefficients a equation ndi tebulo B kuchokera pazomwe zimatsata chizindikirocho zofanana.
- Kenako, timapanga matebulo ena anayi. Aliyense wa iwo ndi buku la matrix. A, makope amenewa ndi okhawo omwe amathandizidwa ndi tebulo B. Gome loyamba lili ndi mzere woyamba, tebulo lachiwiri lili ndi lachiwiri, etc.
- Tsopano tikuyenera kuwerengera komwe kudzapezeketsa magome onsewa. Dongosolo la ma equation limakhala ndi zothetsera pokhapokha ngati onse odziwika ali ndi phindu lina kuposa zero. Kuti muwerengere mtengo, Excel ilinso ndi ntchito ina - MOPANDA. Kapangidwe ka mawu awa ndi motere:
= MOPRED (mndandanda)Chifukwa chake, monga ntchito MOBR, Kutsutsana kokhako ndikuwonetsa tebulo lomwe likukonzedwa.
Chifukwa chake, sankhani selo yomwe ikutsimikizira matrix oyambilira. Kenako dinani batani lodziwa njira zam'mbuyomu "Ikani ntchito".
- Zenera limayatsidwa Ogwira Ntchito. Pitani ku gulu "Masamu" ndipo pakati pa mndandanda wa ogwiritsira ntchito tikuwonetsa dzinalo MOPANDA. Pambuyo pake, dinani batani "Zabwino".
- Tsamba la mkangano wa ntchito likuyamba MOPANDA. Monga mukuwonera, ili ndi gawo limodzi lokha - Menya. Mundime iyi timalowa adilesi ya matrix oyamba osinthika. Kuti muchite izi, ikani cholozera m'munda, kenako sankhani matrix. Pambuyo pake, dinani batani "Zabwino". Ntchito iyi ikuwonetsa zotsatira mu khungu limodzi, osati ambiri, chifukwa chake, kuti muwerenge, simuyenera kusintha kukanikiza kophatikiza Ctrl + Shift + Lowani.
- Ntchitoyi imawerengera zotsalazo ndikuwonetsa mu khungu lomwe lasankhidwa kale. Monga momwe tikuonera, mwa ife ndi omwe amaimira -740, ndiye kuti, silingafanane ndi zero, yomwe imakwanira.
- Momwemonso, timawerengera zomwe zimayimira magome atatu enawo.
- Pamapeto omaliza, timawerengera kutsimikizira kwa matrix oyambira. Mchitidwewu umachitika molingana ndi algorithm yomweyo. Monga mukuwonera, kutsimikizika kwa tebulo loyambirira kumakhalanso ndi nonzero, zomwe zikutanthauza kuti masanjidwewo amawonedwa kuti samatha, ndiye kuti dongosolo la ma equation limakhala ndi mayankho.
- Tsopano ndi nthawi yoti mupeze mizu ya equation. Muzu wa equation uzikhala wofanana ndi mulingo wodziwika wa matrix wolingana osinthidwa mpaka kutsimikizira kwa tebulo loyambirira. Chifukwa chake, kugawanitsa nawonso anayi onse odziwika a matrates osinthidwa ndi chiwerengero -148, komwe ndiko kutsimikizira kwa tebulo loyambirira, timapeza mizu inayi. Monga mukuwonera, ndi ofanana pamakhalidwe 5, 14, 8 ndi 15. Chifukwa chake zimafanana ndendende ndi zomwe tidazipeza pogwiritsa ntchito matris njira 1, yomwe imatsimikizira kulondola kwa yankho la dongosolo la ma equation.
Njira 4: Njira ya Gauss
Makina a equation amathanso kutha kugwiritsa ntchito njira ya Gauss. Mwachitsanzo, tengani dongosolo losavuta la equation kuchokera kuzinthu zitatu zosadziwika:
14x1+2x2+8x3=110
7x1-3x2+5x3=32
5x1+x2-2x3=17
- Apanso, timalemba ma coefficients patebulo A, ndi mawu aulere omwe ali pambuyo pa chikwangwani zofanana - kuyala B. Koma nthawi ino, tidzabweretsa magome onse awiri limodzi, chifukwa tidzazigwiritsa ntchito mtsogolo. Chofunikira ndichakuti mu cell yoyamba ya matrix A mtengo wake unali. Kupanda kutero, muyenera kukonzanso mizere m'malo.
- Koperani mzere woyamba wa matric awiri olumikizana kumizere pansipa (kuti mumveke bwino, mutha kudumpha mzere umodzi). Mu khungu loyamba, lomwe lili pamzere wocheperapo kuposa woyamba, timalowa mu kachitidwe kotsatira:
= B8: E8- $ B $ 7: $ E $ 7 * (B8 / $ B $ 7)Ngati mungakonze matrices mosiyana, ndiye kuti ma adilesi a formula cell azikhala ndi tanthauzo lina, koma mutha kuwerengera ndikuwayerekeza ndi mawonekedwe ndi zithunzi zomwe zaperekedwa pano.
Fomula italowetsedwa, sankhani mzere wonse wamaselo ndikusindikizira kuphatikiza kofunikira Ctrl + Shift + Lowani. Fomula yosankha idzayikidwa mzere ndipo idzadzazidwa ndi mfundo. Chifukwa chake, tidachotsa pamzere wachiwiri woyamba, ochulukitsidwa ndi kuchuluka kwa ma coefficients oyamba amawu awiri oyamba azinthu.
- Pambuyo pake, koperani zingwe zomwe zidatsogolazo ndikununkhira mzere pansipa.
- Sankhani mizere iwiri yoyambira pambuyo pa mzere wakusowa. Dinani batani Copyili pa nthiti mu tabu "Pofikira".
- Timadumphadumpha pambuyo pa kujambula komaliza patsamba. Sankhani khungu loyamba mzere wotsatira. Dinani kumanja. Pazosankha zomwe zikutseguka, sinthani chidziwitso ku "Lowetsani mwapadera". Pamndandanda wowonjezerapo, sankhani malo "Makhalidwe".
- Mzere wotsatira, lowetsani formula. Imatulutsa mzere wachitatu gulu lakale la mzere wachiwiri, kuchulukitsidwa ndi kuchuluka kwa mgawo wachiwiri ndi mzere wachiwiri. M'malo mwathu, kachitidwe kadzakhala ndi mawonekedwe awa:
= B13: E13- $ B $ 12: $ E $ 12 * (C13 / $ C $ 12)Pambuyo polowetsa fomula, sankhani mzere wonse ndikugwiritsa ntchito njira yachidule Ctrl + Shift + Lowani.
- Tsopano muyenera kuyambiranso molingana ndi njira ya Gauss. Timadumpha mizere itatu kuchokera pakalendala yomaliza. Mu mzere wachinayi timalowa pamndandanda wanjira:
= B17: E17 / D17Chifukwa chake, timagawa mzere wotsiriza womwe tidawerengera ndi mgawo wake wachitatu. Mutayimira chilinganizo, sankhani mzere wonse ndikusindikiza kuphatikiza kiyi Ctrl + Shift + Lowani.
- Tipita pamzerewu ndikulowetsa dongosolo lotsatira:
= (B16: E16-B21: E21 * D16) / C16Timakanikizira njira yachidule yokhazikika yokhazikitsa njira.
- Timakweza mzere umodzi pamwambapa. Momwemo timalowetsedwa m'mndandanda wamitundu iyi:
= (B15: E15-B20: E20 * C15-B21: E21 * D15) / B15Komanso sankhani mzere wonse ndikugwiritsa ntchito njira yachidule Ctrl + Shift + Lowani.
- Tsopano tikuwona ziwerengero zomwe zidapezeka mu mzere womaliza wa mizere yomwe tidawerengera koyambirira. Izi ndi ziwerengero (4, 7 ndi 5) adzakhala mizu ya dongosolo lino la equation. Mutha kutsimikizira izi powasinthira m'malo mwa mfundo X1, X2 ndi X3 mwa kufotokoza.
Monga mukuwonera, ku Excel, dongosolo la ma equation limatha kuthetsedwa m'njira zingapo, iliyonse yomwe ili ndi zabwino komanso zovuta zake. Koma njira zonsezi zitha kugawidwa m'magulu akulu awiri: matrix ndikugwiritsa ntchito chida chosankhira paramu. Nthawi zina, njira za matrix sizoyenera nthawi zonse kuthetsa vuto. Makamaka, pamene kudziwa kwa matrix kuli kofanana ndi zero. Nthawi zina, wogwiritsa ntchitoyo amakhala womasuka kusankha njira yomwe angaone kuti ndi yabwino kwa iye.
