Zamkatimu
Matrix ndi gulu la maselo omwe ali pafupi ndi mzake ndipo pamodzi amapanga rectangle. Palibe luso lapadera lomwe limafunikira kuti muzichita zinthu zosiyanasiyana ndi matrix, zofanana ndi zomwe zimagwiritsidwa ntchito pogwira ntchito ndi mtundu wapamwamba ndizokwanira.
Matrix aliwonse ali ndi adilesi yake, yomwe imalembedwa mofanana ndi kuchuluka kwake. Chigawo choyamba ndi selo loyamba lamtundu (lomwe lili pakona yakumanzere), ndipo gawo lachiwiri ndi selo lomaliza, lomwe lili kumunsi kumanja.
Mitundu yambiri
Pantchito zambiri, pogwira ntchito ndi magulu (ndi matrices ndi otero), mafomu amtundu wofananira amagwiritsidwa ntchito. Kusiyanitsa kwawo kwakukulu ndi zomwe zimapangidwira ndikuti zomwe zimatuluka ndi mtengo umodzi wokha. Kuti mugwiritse ntchito fomula yowonjezera, muyenera kuchita zinthu zingapo:
- Sankhani seti ya ma cell omwe ma values adzawonetsedwa.
- Kuyamba kwachindunji kwa chilinganizo.
- Kukanikiza makiyiwo Ctrl + Shift + Enter.
Pambuyo pochita masitepe osavuta awa, fomula yofananira imawonetsedwa mugawo lolowera. Ikhoza kusiyanitsidwa ndi zingwe zopindika mwachizolowezi.
Kuti musinthe, chotsani mafomu osiyanasiyana, muyenera kusankha mtundu womwe mukufuna ndikuchita zomwe mukufuna. Kuti musinthe matrix, muyenera kugwiritsa ntchito kuphatikiza komweko kuti mupange. Pankhaniyi, sizingatheke kusintha chinthu chimodzi chamagulu.
Zomwe zingatheke ndi matrices
Nthawi zambiri, pali zinthu zambiri zomwe zingagwiritsidwe ntchito pa matrices. Tiyeni tione aliyense wa iwo mwatsatanetsatane.
Kutsegula
Anthu ambiri samvetsa tanthauzo la mawu amenewa. Tangoganizani kuti muyenera kusinthana mizere ndi mizati. Izi zimatchedwa transposition.
Musanachite izi, m'pofunika kusankha malo osiyana omwe ali ndi mizere yofanana ndi chiwerengero cha mizati mu matrix oyambirira ndi chiwerengero chofanana cha mizere. Kuti mumvetse bwino momwe izi zimagwirira ntchito, onani chithunzithunzi ichi.
Pali njira zingapo zosinthira.
Njira yoyamba ndi iyi. Choyamba muyenera kusankha masanjidwewo, ndiyeno kukopera izo. Chotsatira, ma cell angapo amasankhidwa pomwe gawo losinthidwa liyenera kuyikidwa. Kenako, zenera la Paste Special limatsegulidwa.
Pali ntchito zambiri kumeneko, koma tiyenera kupeza "Transpose" wailesi batani. Mukamaliza kuchita izi, muyenera kutsimikizira mwa kukanikiza batani la OK.
Palinso njira ina yosinthira matrix. Choyamba muyenera kusankha selo yomwe ili kumtunda kumanzere kwa ngodya yomwe yaperekedwa kwa matrix osinthika. Kenako, bokosi la zokambirana lomwe lili ndi ntchito limatsegulidwa, pomwe pali ntchito Mtengo wa TRANSP. Onani chitsanzo pansipa kuti mudziwe zambiri za momwe mungachitire izi. Mtundu wolingana ndi matrix woyambirira umagwiritsidwa ntchito ngati gawo la ntchito.
Mukadina Chabwino, zidzawonetsa poyamba kuti munalakwitsa. Palibe choyipa mu izi. Izi ndichifukwa choti ntchito yomwe tidayika siyimatanthauzidwa ngati mndandanda wazotsatira. Choncho, tiyenera kuchita zotsatirazi:
- Sankhani gulu la ma cell osungidwira matrix osinthika.
- Dinani batani F2.
- Dinani makiyi otentha Ctrl + Shift + Lowani.
Ubwino waukulu wa njirayi ndi kuthekera kwa matrix osinthika kuti akonze nthawi yomweyo zomwe zili mmenemo, data ikangolowa mu choyambirira. Choncho, tikulimbikitsidwa kugwiritsa ntchito njirayi.
Kuwonjezera
Opaleshoniyi ndi yotheka pokha pokhudzana ndi ma ranges, chiwerengero cha zinthu zomwe zimakhala zofanana. Mwachidule, matrices aliwonse omwe wogwiritsa ntchitoyo azigwira nawo ntchito ayenera kukhala ndi miyeso yofanana. Ndipo timapereka skrini kuti timveke bwino.
Mu matrix omwe akuyenera kukhala, muyenera kusankha selo loyamba ndikuyika fomula.
=Chinthu choyamba cha matrix oyamba + Gawo loyamba la matrix achiwiri
Kenako, timatsimikizira zomwe zalembedwera ndi kiyi ya Enter ndikugwiritsa ntchito auto-complete (bwalo lalikulu lomwe lili pakona yakumanja yakumanja) kukopera zinthu zonse uXNUMXbuXNUMXbilomwe mumatrix watsopano.
Kuwonjezeka
Tiyerekeze kuti tili ndi tebulo lotere lomwe liyenera kuchulukitsidwa ndi 12.
Wowerenga wanzeru amatha kumvetsetsa kuti njirayo ndi yofanana ndi yapitayi. Ndiko kuti, selo lililonse la matrix 1 liyenera kuchulukitsidwa ndi 12 kuti mu matrix omaliza selo iliyonse imakhala ndi mtengo wochulukitsidwa ndi coefficient iyi.
Pankhaniyi, ndikofunikira kutchula maumboni amtundu uliwonse.
Zotsatira zake, fomula yotereyi idzachitika.
=A1*$E$3
Kuphatikiza apo, njirayo ndi yofanana ndi yapitayi. Muyenera kutambasula mtengo uwu ku chiwerengero chofunikira cha maselo.
Tiyerekeze kuti ndikofunikira kuchulukitsa matrices pakati pawo. Koma pali mkhalidwe umodzi wokha umene izi zingatheke. Ndikofunikira kuti chiwerengero cha mizati ndi mizere m'magulu awiriwo awonetsedwe mofanana. Ndiko kuti, ndi mizati ingati, mizere yambiri.
Kuti zikhale zosavuta, tasankha mitundu yokhala ndi matrix omwe amabwera. Muyenera kusuntha cholozera ku selo kumtunda kumanzere ngodya ndi kulowa chilinganizo zotsatirazi =MUMNOH(A9:C13;E9:H11). Musaiwale kukanikiza Ctrl + Shift + Enter.
matrix osiyanasiyana
Ngati mtundu wathu uli ndi mawonekedwe a square (ndiko kuti, kuchuluka kwa maselo molunjika ndi molunjika ndi ofanana), ndiye kuti kudzakhala kotheka kupeza matrix osinthika, ngati kuli kofunikira. Mtengo wake udzakhala wofanana ndi woyamba. Kwa izi, ntchitoyo imagwiritsidwa ntchito Mtengo wa MOBR.
Choyamba, muyenera kusankha selo loyamba la masanjidwewo, momwe chosinthiracho chidzayikidwamo. Nayi chilinganizo =INV(A1:A4). Mtsutsowu umatchula zamtundu womwe tikufunika kupanga matrix osinthika. Zimangokhala kukanikiza Ctrl + Shift + Lowani, ndipo mwamaliza.
Kupeza Determinant ya Matrix
The determinant ndi nambala yomwe ili ndi square matrix. Kuti mufufuze chosankha cha matrix, pali ntchito - MOPRED.
Poyamba, cholozeracho chimayikidwa mu selo iliyonse. Kenako, timalowa =MOPRED(A1:D4)
Zitsanzo zochepa
Kuti timveke bwino, tiyeni tiwone zitsanzo za ntchito zomwe zitha kuchitidwa ndi matrices mu Excel.
Kuchulukitsa ndi kugawa
Njira 1
Tiyerekeze kuti tili ndi matrix A omwe ali ndi maselo atatu okwera ndi ma cell anayi m'lifupi. Palinso nambala k, yomwe imalembedwa mu selo lina. Pambuyo pochita ntchito yochulukitsa matrix ndi nambala, zikhalidwe zingapo zimawonekera, zokhala ndi miyeso yofanana, koma gawo lililonse limachulukitsidwa ndi k.
Mtundu B3: E5 ndiye matrix oyambilira omwe adzachulukitsidwe ndi nambala k, yomwe ili mu cell H4. Zotsatira zake zidzakhala mu K3:N5. Matrix oyambirira adzatchedwa A, ndipo zotsatira zake - B. Chotsatiracho chimapangidwa mwa kuchulukitsa matrix A ndi nambala k.
Kenako, kulowa =B3*$H$4 ku cell K3, pomwe B3 ndi element A11 ya matrix A.
Musaiwale kuti selo H4, pomwe nambala k ikuwonetsedwa, iyenera kulowetsedwa mu fomula pogwiritsa ntchito chidziwitso chonse. Kupanda kutero, mtengowo udzasintha pamene gululo likukopera, ndipo zotsatira zake zidzalephera.
Kenako, chikhomo chodzaza zokha (mzere womwewo pakona yakumanja yakumanja) chimagwiritsidwa ntchito kukopera mtengo womwe wapezeka mu selo K3 kumaselo ena onse mumndandandawu.
Chifukwa chake tidatha kuchulukitsa matrix A ndi nambala inayake ndikupeza matrix B.
Kugawikana kumachitika mofananamo. Mukungoyenera kuyika fomula yogawa. Kwa ife, izi =B3/$H$4.
Njira 2
Choncho, kusiyana kwakukulu kwa njirayi ndikuti zotsatira zake zimakhala zambiri, choncho muyenera kugwiritsa ntchito ndondomekoyi kuti mudzaze maselo onse.
Ndikofunikira kusankha mtundu wotsatira, lowetsani chizindikiro chofanana (=), sankhani ma cell omwe ali ndi miyeso yolingana ndi matrix oyamba, dinani nyenyezi. Kenako, sankhani cell yokhala ndi nambala k. Chabwino, kuti mutsimikizire zochita zanu, muyenera kukanikiza makiyi omwe ali pamwambapa. Hooray, mndandanda wonse ukudzaza.
Kugawanika kumachitika mofananamo, chizindikiro chokha * chiyenera kusinthidwa ndi /.
Kuwonjezera ndi kuchotsa
Tiyeni tifotokoze zitsanzo zothandiza za kugwiritsa ntchito njira zowonjezera ndi zochotsera pochita.
Njira 1
Musaiwale kuti ndizotheka kuwonjezera matrices omwe kukula kwawo kuli kofanana. Pazotsatira zake, ma cell onse amadzazidwa ndi mtengo womwe ndi kuchuluka kwa maselo ofanana mu matrices oyambilira.
Tiyerekeze kuti tili ndi matrices awiri omwe ali ndi 3 × 4 kukula kwake. Kuti muwerenge kuchuluka kwake, muyenera kuyika fomula ili mu cell N3:
=B3+H3
Apa, chinthu chilichonse ndi selo loyamba la matrices omwe tiwonjezere. Ndikofunika kuti maulalowo akhale achibale, chifukwa ngati mugwiritsa ntchito maulalo amtheradi, zolondola sizidzawonetsedwa.
Kupitilira apo, mofanana ndi kuchulukitsa, pogwiritsa ntchito chikhomo chokhazikika, timafalitsa fomula kumaselo onse a matrix omwe atuluka.
Kuchotsa kumachitidwa mofananamo, kupatulapo kuti chikwangwani chochotsa (-) chimagwiritsidwa ntchito osati chizindikiro chowonjezera.
Njira 2
Mofanana ndi njira yowonjezerera ndi kuchotsa matrices awiri, njirayi imaphatikizapo kugwiritsa ntchito njira yotsatizana. Chifukwa chake, zotsatira zake, kuchuluka kwazinthu zauXNUMXbuXNUMX kudzaperekedwa nthawi yomweyo. Choncho, simungathe kusintha kapena kuchotsa zinthu zilizonse.
Choyamba muyenera kusankha mtundu wolekanitsidwa chifukwa cha masanjidwewo, kenako dinani "="". Kenako muyenera kufotokoza gawo loyamba la chilinganizo mu mawonekedwe a matrix A, dinani chizindikiro + ndikulemba gawo lachiwiri mu mawonekedwe amitundu yofananira ndi matrix B. Timatsimikizira zochita zathu mwa kukanikiza kuphatikiza. Ctrl + Shift + Lowani. Chilichonse, tsopano matrix onse obwerawo ali odzazidwa ndi zikhalidwe.
Chitsanzo cha kusintha kwa matrix
Tiyerekeze kuti tifunika kupanga matrix AT kuchokera ku matrix A, omwe tili nawo poyambirira. Womalizayo ali, kale ndi mwambo, miyeso ya 3 × 4. Kwa izi tidzagwiritsa ntchito =TRANSP().
Timasankha mitundu yama cell a matrix AT.
Kuti muchite izi, pitani ku tabu ya "Formulas", pomwe sankhani "Ikani ntchito", pezani gulu la "References and arrays" ndikupeza ntchitoyo. Mtengo wa TRANSP. Pambuyo pake, zochita zanu zimatsimikiziridwa ndi batani la OK.
Kenaka, pitani kuwindo la "Function Arguments", pomwe mndandanda wa B3: E5 umalowetsedwa, womwe umabwereza matrix A. Kenako, muyenera kukanikiza Shift + Ctrl, ndiyeno dinani "Chabwino".
Ndikofunika. Simuyenera kukhala waulesi kukanikiza makiyi otentha awa, chifukwa apo ayi, mtengo wa cell yoyamba yamitundu yosiyanasiyana ya AT matrix udzawerengedwa.
Zotsatira zake, timapeza tebulo losinthika lomwe limasintha mayendedwe ake pambuyo pa loyambirira.
Kusaka kwa Inverse Matrix
Tiyerekeze kuti tili ndi matrix A, omwe ali ndi kukula kwa 3 × 3 maselo. Tikudziwa kuti kuti tipeze matrix osinthika, tiyenera kugwiritsa ntchito ntchitoyi =MOBR().
Tsopano tikufotokoza momwe tingachitire izi muzochita. Choyamba muyenera kusankha mtundu wa G3: I5 (matrix osinthika adzakhala pamenepo). Muyenera kupeza chinthu cha "Insert Function" pa tabu ya "Formulas".
Nkhani ya "Insert function" idzatsegulidwa, pomwe muyenera kusankha gulu la "Math". Ndipo padzakhala ntchito mu mndandanda Mtengo wa MOBR. Tikasankha, tiyenera kukanikiza kiyi OK. Kenaka, bokosi la "Function Arguments" likuwonekera, momwe timalemba mndandanda wa B3: D5, womwe umagwirizana ndi matrix A. Zochita zina ndizofanana ndi kusintha. Muyenera kukanikiza kuphatikiza kiyi Shift + Ctrl ndikudina Chabwino.
Mawuwo
Tapenda zitsanzo za momwe mungagwirire ntchito ndi matrices mu Excel, ndikufotokozeranso chiphunzitsocho. Zikuwoneka kuti izi sizowopsa monga momwe zingawonekere poyang'ana koyamba, sichoncho? Zimangomveka zosamvetsetseka, koma kwenikweni, wogwiritsa ntchito wamba amayenera kuthana ndi matrices tsiku lililonse. Zitha kugwiritsidwa ntchito pafupifupi tebulo lililonse pomwe pali deta yaying'ono. Ndipo tsopano mukudziwa momwe mungachepetsere moyo wanu pogwira nawo ntchito.