Ƙaddamarwa a cikin OpenOffice Writer. Quick Fara Guide

Rashin ikon warware tsarin tsarin daidaituwa na iya zama mai amfani ba kawai a makaranta, amma har ma a aikace. Bugu da ƙari, ba kowane mai amfani da PC ya san cewa Excel yana da nasa mafita don lissafin linzamin. Bari mu gano yadda za mu yi amfani da wannan kayan aiki na kwamfutar hannu don aiwatar da wannan aiki a hanyoyi daban-daban.

Ayyuka

Duk wata daidaituwa za a iya la'akari da gyara kawai idan aka samo asali. A cikin Excel, akwai zaɓuɓɓuka masu yawa don gano tushen. Bari mu dubi kowanensu.

Hanyar 1: Hanyar Matrix

Hanyar da ta fi dacewa don warware tsarin tsarin layi tare da kayan aikin Excel shine don amfani da hanyar matrix. Ya ƙunshi gina wani matakan daga mahaɗin maganganu, sa'an nan kuma a ƙirƙirar matrix mara kyau. Bari mu yi kokarin amfani da wannan hanyar don warware tsarin tsarin daidaitawa:


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

1. Mun cika matrix tare da lambobin da suke hadewa na lissafin. Wadannan lambobin ya kamata a tsara ta yadda za su kasance, don la'akari da wurin da kowane tushe ya dace. Idan an bayyana wani daga cikin tushen asali, to a cikin wannan yanayin ana ɗaukar ma'auni daidai da zero. Idan ba a nuna mahaɗin a cikin daidaitattun ba, amma tushen da ya dace, ba a samu ba, ana ɗauka cewa mahaɗin yana daidaita da 1. Sake tebur mai ɗaukar kayan aiki azaman samfurin A.



2. Mahimmanci, muna rubuta dabi'u bayan daidai alamar. Sanya su ta hanyar suna dayawa azaman zane B.



3. Yanzu, don gano tushen asalin, na farko, muna buƙatar samun matrix, ƙin abin da ke faruwa. Abin farin cikin, a Excel akwai mai sana'a na musamman wanda aka tsara don magance matsalar. An kira MOBR. Yana da daidaito mai sauƙi:

   = MBR (tsararru)

   Magana "Array" - wannan shi ne, a gaskiya, adireshin tushen launi.

   Saboda haka, za mu zaɓa a kan takardar wata yanki na kullun kullun, wanda yake daidai da girman zuwa iyakar matrix na ainihi. Danna maballin "Saka aiki"located kusa da dabara bar.



4. Gudun Ma'aikata masu aiki. Je zuwa category "Ilmin lissafi". A cikin jerin muna neman sunan "MOBR". Bayan an samo shi, zaɓi shi kuma danna maballin. "Ok".



5. Gidan gwajin aikin ya fara. MOBR. Tana da filin daya kawai ta yawan yawan muhawara - "Array". A nan kana buƙatar saka adireshin teburinmu. Domin waɗannan dalilai, saita siginan kwamfuta a wannan filin. Daga nan sai mu riƙe maɓallin linzamin hagu kuma zaɓi yankin a kan takardar da aka samo matrix. Kamar yadda kake gani, ana shigar da bayanan da aka sanya akan wurin a cikin taga. Bayan kammala wannan aikin, mafi mahimmanci shine danna maballin. "Ok"amma kada ku rush. Gaskiyar ita ce, danna wannan maballin daidai yake da amfani da umurnin Shigar. Amma a yayin da kake aiki tare da bayanan bayan kammala karatun wannan tsari, kada ka danna maballin. Shigarda kuma samar da saiti na maɓallan gajeren hanya Ctrl + Shigar + Shigar. Yi wannan aiki.



6. Saboda haka, bayan wannan, shirin yana yin lissafi kuma a cikin fitarwa a cikin wurin da aka zaɓa kafin mu zaɓa da nauyin matrix.



7. Yanzu za mu buƙaci mu ninka matrix mara kyau ta matrix. Bwanda ya ƙunshi ɗaya shafi na dabi'u bayan bayanan daidai a cikin maganganu. Don ƙaddamar da tebur a Excel yana da aiki na dabam, wanda aka kira Mummy. Wannan sanarwa tana da wadannan haɗin kai:

   = MUMNOGUE (Array1; Array2)

   Zaži kewayon, a cikin yanayinmu wanda ya ƙunshi nau'i hudu. Sa'an nan kuma sake gudu Wizard aikinta danna gunkin "Saka aiki".



8. A cikin rukunin "Ilmin lissafi"gudu Ma'aikata masu aikizaɓi sunan "MUMNOZH" kuma danna maballin "Ok".



9. An kunna maɓallin maganin aikin. Mummy. A cikin filin "Massive1" shigar da daidaitawar matrix ɗinmu mara kyau. Don yin wannan, kamar lokaci na ƙarshe, saita siginan kwamfuta a filin kuma tare da maɓallin linzamin kwamfuta na hagu da aka ajiye, zaɓi tebur daidai da siginan kwamfuta. Ana gudanar da wani irin wannan aikin don yin daidaito a filin "Massiv2", kawai a wannan lokacin za mu zaɓi dabi'un shafi. B. Bayan an dauki ayyukan da aka yi a sama, kuma ba mu da sauri don danna maballin "Ok" ko key Shigar, da kuma rubuta maɓallin haɗin Ctrl + Shigar + Shigar.



10. Bayan wannan aikin, tushen asalin ya bayyana a cikin cell da aka zaɓa: X1, X2, X3 kuma X4. Za a shirya su cikin jerin. Saboda haka, zamu iya cewa mun warware wannan tsarin. Don tabbatar da daidaitattun bayani, ya isa ya sauya amsoshin da aka ba su cikin tsarin asalin asali maimakon maimakon asali. Idan an daidaita daidaito, wannan yana nufin cewa an tsara tsarin daidaitaccen tsari daidai.

Darasi: Kashe Matel na Excel

Hanyar 2: zaɓi na sigogi

Hanyar da aka sani na biyu don warware tsarin tsarin daidaituwa a Excel shine amfani da hanyar zaɓin hanyar zabin. Dalilin wannan hanya ita ce bincika kishiyar. Wato, bisa ga sakamakon da aka sani, muna nemo wata hujja mara sani. Bari mu yi amfani da daidaitattun quadratic misali.

3x ^ 2 + 4x-132 = 0

1. Karɓi darajar x don daidaita 0. Yi lissafin adadin daidai da shi f (x)ta hanyar yin amfani da wannan tsari:

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

   Maimakon darajar "X" canza adireshin tantanin halitta inda aka samo lambar 0dauka da mu don x.



2. Jeka shafin "Bayanan". Muna danna maɓallin "Analysis" idan idan. An sanya wannan button a kan rubutun a cikin akwatin kayan aiki. "Yin aiki tare da bayanai". Jerin jerin zaɓuka ya buɗe. Zaɓi matsayi a ciki "Zaɓaɓɓen zaɓi ...".



3. Zaɓin zaɓi na zaɓi na farawa. Kamar yadda kake gani, ya ƙunshi nau'i uku. A cikin filin "Shigar a cikin tantanin halitta" saka adireshin tantanin halitta inda aka samo asali f (x)ƙididdige ta wurin mu kadan a baya. A cikin filin "Darajar" shigar da lambar "0". A cikin filin "Canji Canja" saka adireshin tantanin salula inda darajar ta kasance xa baya aka karɓa ta hanyar mu don 0. Bayan yin waɗannan ayyuka, danna kan maballin "Ok".



4. Bayan haka, Excel zai yi lissafi ta amfani da zaɓin zabin. Wannan zai sanar da alamar bayani. Ya kamata danna kan maballin "Ok".



5. Sakamakon lissafta tushen asalin zai kasance cikin tantanin da muka sanya a cikin filin "Canji Canja". A cikin yanayinmu, kamar yadda muke gani x zai zama daidai da 6.

Wannan sakamakon za a iya bincika ta hanyar sauya wannan darajar a cikin maganganun da aka zaɓa a maimakon ƙimar x.

Darasi: Zaɓin zaɓi na Excel

Hanyar 3: Hanyar Cramer

Yanzu za mu yi kokarin warware tsarin tsarin daidaitaccen tsarin Kramer. Alal misali, bari mu ɗauki tsarin da aka yi amfani dashi Hanyar 1:


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

1. Kamar yadda a cikin hanyar farko, muna yin matrix A daga coefficients na equations da tebur B na dabi'u da ke bi alamar daidai.



2. Bugu da ƙari za mu yi tebur huɗu. Kowannensu yana kwafin matrix. A, kawai waɗannan kofe suna da ɗayan shafi a biyun da aka maye gurbin da tebur B. A cikin teburin farko shi ne shafi na farko, a cikin tebur na biyu shi ne na biyu, da sauransu.



3. Yanzu muna buƙatar lissafta masu ƙayyadewa ga dukan waɗannan tebur. Tsarin lissafin zasu sami mafita kawai idan duk masu kayyade suna da darajar sauran zero. Don ƙidaya wannan darajar a cikin Excel sake akwai aiki na dabam - SANTA. Maganar wannan bayani shine kamar haka:

   = SASHI (tsararru)

   Saboda haka, kamar aikin MOBR, kawai gardama shine batun yin la'akari da tebur.

   Don haka, zaɓi tantanin halitta wanda za'a iya nuna mahimmancin matrix na farko. Sa'an nan kuma danna maɓallin da aka saba daga hanyoyin da suka gabata. "Saka aiki".



4. Window aiki Ma'aikata masu aiki. Je zuwa category "Ilmin lissafi" kuma daga cikin jerin masu aiki, zaɓi sunan a can MOPRED. Bayan haka, danna maballin "Ok".



5. Gidan gwajin aikin ya fara. SANTA. Kamar yadda ka gani, yana da filin guda daya - "Array". Shigar da adireshin matakan da aka canza zuwa wannan filin. Don yin wannan, saita siginan kwamfuta a filin, sannan ka zaɓa maɓallin matrix. Bayan haka, danna maballin "Ok". Wannan aikin yana nuna sakamakon a cikin sel guda, maimakon tsararru, don haka don samun lissafi, baka buƙatar komawa don danna maɓallin haɗin Ctrl + Shigar + Shigar.



6. Ayyukan na lissafa sakamakon kuma nuna shi a cikin wani zaɓi da aka zaɓa. Kamar yadda muka gani, a yanayinmu, mai ƙayyadewa shine -740, wato, ba daidai ba ne da siffar da ta dace da mu.



7. Hakazalika, muna lissafin masu ƙayyadewa don sauran Tables uku.



8. A mataki na ƙarshe, muna lissafta mai ƙayyade na matrix na farko. Hanyar shine duk algorithm. Kamar yadda muka gani, ma'auni na firamare na farko shi ma nonzero ne, wanda ke nufin cewa ana daukar matrix ba a matsayin wanda ba a haɗa ba, wato, tsarin tsarin daidaitawa yana da mafita.



9. Yanzu lokaci ya yi don gano tushen asalin. Tushen lissafi zai zama daidai da rabo daga mai ƙayyade matakan da aka canzawa daidai zuwa mai ƙayyade na tebur na farko. Ta haka ne, rarraba gaba ɗaya dukkan nau'ikan ma'auni huɗu na matrices da aka canza ta lamba -148wanda shine ma'auni na tebur na asali, muna samo asali hudu. Kamar yadda kake gani, suna daidaita da dabi'u 5, 14, 8 kuma 15. Saboda haka, suna daidai daidai da tushen da muka samo ta amfani da matrix mara kyau a cikin Hanyar 1wanda ya tabbatar da daidaiwar maganin tsarin tsarin.

Hanyar 4: Hanyar Gauss

Za'a iya warware tsarin tsarin daidaitawa ta hanyar amfani da hanyar Gauss. Alal misali, bari mu dauki tsarin da ya fi sauƙi daga daidaitattun abubuwa uku:


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

1. Bugu da ƙari muna rubutun masu kwakwalwa a kan tebur. Ada mambobi mamba bayan alamar daidai - ga tebur B. Amma a wannan lokacin zamu zo da tebur biyu tare, tun da muna bukatar wannan don kara aiki. Wani muhimmin yanayin ita ce, a cikin wayar farko ta matrix A Darajar ba ta da kome ba. In ba haka ba, sake shirya layin.



2. Kwafi jeri na farko na matayen da aka haɗu biyu a cikin layin da ke ƙasa (don tsabta, za ku iya tsallake wata jere). A cikin wayar farko, wadda take a cikin layin har ma da ƙasa da na baya, shigar da wannan tsari:

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

   Idan kun shirya matrixes daban-daban, to, adireshin da ke cikin ma'anar za ku sami ma'anar daban, amma za ku iya lissafta su, kwatanta su da dabarar da hotuna da aka gabatar a nan.

   Bayan an shigar da wannan tsari, zaɓi dukan jeri na sel kuma latsa maɓallin haɗin Ctrl + Shigar + Shigar. Za'a yi amfani da matakan tsararren a jere kuma za'a cika da dabi'u. Sabili da haka, mun janye daga layin na biyu na farko, karuwa ta hanyar haɗin gwargwadon farko na maganganun farko na tsarin.



3. Bayan haka, kwafa maɗaukaki mai layi sannan a manna shi cikin layin da ke ƙasa.



4. Zaɓi layi biyu biyu bayan layin da aka rasa. Muna danna maɓallin "Kwafi"wanda yake a kan rubutun a cikin shafin "Gida".



5. Muna kayar da layin bayan shigarwa ta ƙarshe akan takardar. Zaɓi sel na farko a cikin layi na gaba. Danna maballin linzamin dama. A cikin jerin mahallin da aka bude, motsa siginan kwamfuta zuwa abu "Manna Musamman". A cikin jerin ƙarin ƙarin, zaɓi matsayi "Darajar".



6. A cikin layi na gaba, shigar da maɓallin lissafi. Ya karɓa daga jere na uku na ƙungiyar bayanai na baya jigon na biyu ya karu ta hanyar rabo na kashi na biyu na jere na uku da na biyu. A cikin yanayinmu, wannan tsari zai kasance kamar haka:

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

   Bayan shigar da dabara, zaɓi dukan jerin kuma amfani da maɓallin gajeren hanya Ctrl + Shigar + Shigar.



7. Yanzu wajibi ne a kashe kullun yadda ya kamata bisa ga hanya na Gauss. Tsallake layi uku daga shigarwa ta karshe. A cikin layi na huɗu, shigar da maɓallin tsari:

   = B17: E17 / D17

   Ta haka ne, muna rarraba layin da ta ƙarshe ta kirkiro ta hanyar mu na uku. Bayan buga rubutu, zaɓi dukkan layin kuma danna maɓallin haɗin Ctrl + Shigar + Shigar.



8. Muna daukaka layin kuma shigar da shi a cikin wannan tsari:

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

   Mun danna maɓallin mabuɗin haɗi don yin amfani da madadin lissafi.



9. Mun tashi ɗaya layin sama. A ciki mun shigar da madadin lissafi na nau'i mai biyowa:

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

   Bugu da sake, zaɓi dukan layin kuma amfani da gajeren hanya Ctrl + Shigar + Shigar.



10. Yanzu muna duban lambobin da aka juya a cikin shafi na ƙarshe na asalin rukunin layuka, waɗanda aka ƙidayar da mu a baya. Waɗannan lambobi ne (4, 7 kuma 5) zai zama asalin wannan tsarin tsarin. Zaka iya duba wannan ta hanyar canza su don dabi'u. X1, X2 kuma X3 a cikin maganganu.

Kamar yadda kake gani, a cikin Excel, ana iya warware tsarin tsarin daidaituwa a hanyoyi da yawa, kowannensu yana da nasarorin da ba shi da amfani. Amma duk waɗannan hanyoyi za a iya raba zuwa manyan kungiyoyi biyu: matrix da amfani da kayan zaɓin saitin. A wasu lokuta, hanyoyin matrix ba su dacewa da kyau don warware matsalar ba. Musamman ma, lokacin da ma'auni na matrix ba kome ba ne. A wasu lokuta, mai amfani yana da 'yanci don yanke shawarar wane zaɓi ya ɗauki mafi dacewa da kansa.