Contents
Matrix wani tsari ne na sel wanda ke kusa da juna kai tsaye kuma waɗanda tare suka samar da rectangle. Ba a buƙatar ƙwarewa na musamman don yin ayyuka daban-daban tare da matrix, daidai da waɗanda aka yi amfani da su lokacin aiki tare da kewayon gargajiya sun isa.
Kowane matrix yana da adireshin kansa, wanda aka rubuta ta hanyar da ke cikin kewayon. Bangaren farko shine tantanin halitta na farko na kewayon (wanda yake a kusurwar hagu na sama), sashi na biyu kuma shine tantanin halitta na ƙarshe, wanda yake a kusurwar dama ta ƙasa.
Tsarukan tsari
A cikin mafi yawan ayyuka, lokacin aiki tare da tsararru (kuma matrices suna da irin wannan), ana amfani da ƙididdiga na nau'in da ya dace. Bambancinsu na asali daga na yau da kullun shine cewa fitarwa ta ƙarshe ƙima ɗaya ce kawai. Don amfani da dabarar tsararru, kuna buƙatar yin wasu abubuwa:
- Zaɓi saitin sel inda za'a nuna ƙimar.
- Gabatarwar dabarar kai tsaye.
- Danna maɓallin maɓallin Ctrl + Shift + Shigar.
Bayan yin waɗannan matakai masu sauƙi, ana nuna tsarin tsarawa a cikin filin shigarwa. Ana iya bambanta shi da takalmin gyaran kafa na yau da kullum.
Don gyarawa, share tsarin tsarawa, kuna buƙatar zaɓar kewayon da ake buƙata kuma kuyi abin da kuke buƙata. Don gyara matrix, kuna buƙatar amfani da haɗin haɗin guda ɗaya don ƙirƙirar shi. A wannan yanayin, ba zai yiwu a gyara kashi ɗaya na tsararrun ba.
Abin da za a iya yi tare da matrices
Gabaɗaya, akwai adadi mai yawa na ayyuka waɗanda za a iya amfani da su ga matrices. Bari mu dubi kowannensu dalla-dalla.
Canza
Mutane da yawa ba su fahimci ma'anar wannan kalma ba. Ka yi tunanin cewa kana buƙatar musanya layuka da ginshiƙai. Ana kiran wannan aikin transposition.
Kafin yin haka, ya zama dole a zaɓi wani yanki daban wanda ke da adadin layuka iri ɗaya kamar adadin ginshiƙai a cikin matrix na asali da kuma adadin ginshiƙan. Don ƙarin fahimtar yadda wannan ke aiki, kalli wannan hoton allo.
Akwai hanyoyi da yawa don yadda ake jujjuyawa.
Hanya ta farko ita ce mai zuwa. Da farko kuna buƙatar zaɓar matrix, sannan ku kwafi shi. Bayan haka, ana zaɓar kewayon sel inda yakamata a saka kewayon da aka yi. Bayan haka, taga Manna Special yana buɗewa.
Akwai ayyuka da yawa a wurin, amma muna buƙatar nemo maɓallin rediyon “Transpose”. Bayan kammala wannan aikin, kuna buƙatar tabbatar da shi ta danna maɓallin Ok.
Akwai wata hanya don jujjuya matrix. Da farko kuna buƙatar zaɓar tantanin halitta da ke cikin kusurwar hagu na sama na kewayon da aka keɓe don matrix ɗin da aka canjawa. Bayan haka, akwatin maganganu yana buɗewa tare da ayyuka, inda akwai aiki TRANSP. Dubi misalin da ke ƙasa don ƙarin cikakkun bayanai kan yadda ake yin hakan. Ana amfani da kewayon da ya dace da matrix na asali azaman siga na aiki.
Bayan danna Ok, zai fara nuna cewa kun yi kuskure. Babu wani abu mai muni a cikin wannan. Wannan saboda aikin da muka saka ba a bayyana shi azaman tsarin tsararru ba. Don haka, muna buƙatar yin abubuwa kamar haka:
- Zaɓi saitin sel waɗanda aka tanadar don matrix ɗin da aka canjawa.
- Danna maɓallin F2.
- Danna maɓallan zafi Ctrl + Shift + Shigar.
Babban fa'idar hanyar shine ikon matrix ɗin da aka canjawa wuri don gyara bayanan da ke cikinsa nan da nan, da zarar an shigar da bayanan cikin ainihin. Saboda haka, ana ba da shawarar yin amfani da wannan hanya.
Bugu da kari
Wannan aiki yana yiwuwa ne kawai dangane da waɗancan jeri, adadin abubuwan da ke cikin su iri ɗaya ne. A taƙaice, kowane matrices ɗin da mai amfani zai yi aiki da su dole ne ya kasance yana da girma iri ɗaya. Kuma muna ba da hoton allo don tsabta.
A cikin matrix wanda ya kamata ya fito, kuna buƙatar zaɓar tantanin halitta na farko kuma shigar da irin wannan dabarar.
=Kashi na farko na matrix na farko + Kashi na farko na matrix na biyu
Na gaba, mun tabbatar da shigarwar dabarar tare da maɓallin Shigar kuma amfani da auto-cikakke (square a cikin ƙananan kusurwar dama) don kwafi duk darajar uXNUMXbuXNUMXbinto sabon matrix.
Yawaita
A ce muna da irin wannan teburi wanda yakamata a ninka shi da 12.
Mai karatu mai hankali zai iya fahimtar cewa hanyar ta yi kama da wacce ta gabata. Wato kowane sel na matrix 1 dole ne a ninka shi da 12 ta yadda a cikin matrix na ƙarshe kowane tantanin halitta yana ɗauke da ƙimar da aka ninka ta wannan ƙima.
A wannan yanayin, yana da mahimmanci a ƙayyade cikakkun bayanan tantanin halitta.
A sakamakon haka, irin wannan tsari zai juya.
=A1*$E$3
Bugu da ari, dabarar tayi kama da na baya. Kuna buƙatar shimfiɗa wannan ƙimar zuwa adadin da ake buƙata na sel.
Bari mu ɗauka cewa wajibi ne a ninka matrices a tsakaninsu. Amma akwai sharadi ɗaya kawai wanda hakan zai yiwu a ƙarƙashinsa. Ya zama dole cewa adadin ginshiƙai da layuka a cikin jeri biyu su kasance da kamanni iri ɗaya. Wato, ginshiƙai nawa, layuka masu yawa.
Don yin shi mafi dacewa, mun zaɓi kewayon tare da matrix sakamakon. Kuna buƙatar matsar da siginan kwamfuta zuwa tantanin halitta a kusurwar hagu na sama kuma shigar da dabara mai zuwa = MUMNOH(A9:C13;E9:H11). Kar a manta latsa Ctrl + Shift + Shigar.
inverse matrix
Idan kewayon mu yana da siffar murabba'i (wato, adadin sel a kwance da a tsaye iri ɗaya ne), to, zai yiwu a sami matrix mai juzu'i, idan ya cancanta. Darajarsa za ta yi kama da na asali. Don wannan, ana amfani da aikin MOBR.
Don fara da, ya kamata ka zaɓi tantanin halitta na farko na matrix, wanda za a shigar da inverse. Ga dabarar =INV(A1:A4). Hujjar tana ƙayyadaddun kewayon da muke buƙatar ƙirƙirar matrix juzu'i. Ya rage kawai don danna Ctrl + Shift + Shigar, kuma kun gama.
Nemo Ƙaddamar da Matrix
Ƙididdigar lamba ita ce matrix mai murabba'i. Don nemo mai ƙayyade matrix, akwai aiki - MOPRED.
Da farko, ana sanya siginan kwamfuta a kowace tantanin halitta. Na gaba, mu shiga =MOPRED(A1:D4)
Bayanan misalai
Don ƙarin bayani, bari mu kalli wasu misalan ayyukan da za a iya yi tare da matrices a cikin Excel.
Yawan yawa da rarrabawa
Hanyar 1
A ce muna da matrix A wanda yake da tsayin sel uku da faɗin sel huɗu. Akwai kuma lamba k, wadda aka rubuta a wani tantanin halitta. Bayan aiwatar da aikin ninka matrix da lamba, za a bayyana kewayon dabi'u, suna da nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan nau'ikan za su bayyana da k.
Kewayon B3:E5 shine matrix na asali wanda za'a ninka ta lambar k, wanda kuma yana cikin cell H4. Sakamakon matrix zai kasance a cikin kewayon K3: N5. Za a kira matrix na farko A, kuma wanda ya haifar - B. An kafa na ƙarshe ta hanyar ninka matrix A ta lamba k.
Gaba, shiga =B3*$H$4 zuwa cell K3, inda B3 shine kashi A11 na matrix A.
Kar a manta cewa tantanin halitta H4, inda aka nuna lambar k, dole ne a shigar da su cikin dabara ta amfani da cikakkiyar tunani. In ba haka ba, ƙimar za ta canza lokacin da aka kwafi tsararrun, kuma matrix ɗin da aka samu zai gaza.
Bayan haka, ana amfani da alamar autofill (jiki ɗaya a cikin ƙananan kusurwar dama) don kwafin ƙimar da aka samu a cikin tantanin halitta K3 zuwa duk sauran sel a cikin wannan kewayon.
Don haka mun sami nasarar ninka matrix A ta wani lamba kuma mu sami matrix B.
Ana aiwatar da rabo ta hanyar irin wannan. Kuna buƙatar shigar da tsarin rarraba kawai. A wurinmu, wannan = B3/$H$4.
Hanyar 2
Don haka, babban bambance-bambancen wannan hanyar shine cewa sakamakon shine tarin bayanai, don haka kuna buƙatar amfani da tsarin tsararru don cika duka saitin sel.
Wajibi ne don zaɓar kewayon da aka samu, shigar da alamar daidai (=), zaɓi saitin sel tare da ma'aunin da ya dace da matrix na farko, danna tauraro. Na gaba, zaɓi tantanin halitta mai lamba k. To, don tabbatar da ayyukanku, dole ne ku danna haɗin maɓallin da ke sama. Hooray, duk kewayon yana cika.
Ana aiwatar da rarraba ta irin wannan hanya, kawai alamar * dole ne a maye gurbinsu da /.
Ƙara da ragi
Bari mu bayyana wasu misalai masu amfani na amfani da hanyoyin ƙari da ragi a aikace.
Hanyar 1
Kar ka manta cewa yana yiwuwa a ƙara kawai waɗancan matrices waɗanda girmansu iri ɗaya ne. A cikin kewayon da aka samu, duk sel suna cike da ƙima wanda shine jimlar sel iri ɗaya a cikin matrices na asali.
A ce muna da matrices biyu masu girman 3 × 4. Don ƙididdige jimlar, yakamata ku saka wannan dabara a cikin tantanin halitta N3:
= B3+H3
Anan, kowane kashi shine tantanin halitta na farko na matrices waɗanda za mu ƙara. Yana da mahimmanci cewa hanyoyin haɗin gwiwa sun kasance dangi, saboda idan kun yi amfani da cikakkun hanyoyin haɗin gwiwa, ba za a nuna daidaitattun bayanai ba.
Bugu da ari, kama da ninkawa, ta amfani da alamar autocomplete, muna yada dabarar zuwa duk sel na matrix sakamakon.
Ana yin ragi ta hanya iri ɗaya, ban da kawai cewa ana amfani da alamar ragi (-) maimakon alamar ƙari.
Hanyar 2
Hakazalika hanyar ƙarawa da rage matrices biyu, wannan hanyar ta ƙunshi amfani da dabarar tsararru. Saboda haka, a sakamakonsa, za a fitar da saitin ƙimar uXNUMXbuXNUMXb nan take. Don haka, ba za ku iya gyara ko share kowane abubuwa ba.
Da farko kuna buƙatar zaɓar kewayon da aka raba don matrix sakamakon, sannan danna "=". Sa'an nan kuma kana buƙatar ƙayyade ma'aunin farko na dabarar a cikin nau'i na kewayon matrix A, danna alamar + kuma rubuta siga na biyu a cikin nau'i na kewayon daidai da matrix B. Muna tabbatar da ayyukanmu ta hanyar latsa haɗin. Ctrl + Shift + Shigar. Komai, yanzu duk matrix sakamakon yana cike da ƙima.
Matrix transposition misali
Bari mu ce muna buƙatar ƙirƙirar matrix AT daga matrix A, wanda muke da shi da farko ta hanyar juyawa. Ƙarshen yana da, ta hanyar al'ada, ma'auni na 3 × 4. Don wannan za mu yi amfani da aikin =TRANSP().
Mun zaɓi kewayon sel na matrix AT.
Don yin wannan, je zuwa shafin "Formulas", inda za a zabi "Saka ayyuka", a can nemo sashen "References da arrays" kuma sami aikin. TRANSP. Bayan haka, ana tabbatar da ayyukanku tare da maɓallin Ok.
Na gaba, je zuwa taga "Ayyukan Arguments", inda aka shigar da kewayon B3: E5, wanda ke maimaita matrix A. Na gaba, kuna buƙatar danna Shift + Ctrl, sannan danna "Ok".
Yana da muhimmanci. Kada ku yi kasala don danna waɗannan maɓallan zafi, saboda in ba haka ba kawai za a ƙididdige ƙimar tantanin halitta na farko na kewayon AT matrix.
A sakamakon haka, muna samun irin wannan tebur mai jujjuyawa wanda ke canza ƙimar sa bayan na asali.
Binciken Matrix Inverse
A ce muna da matrix A, wanda ke da girman sel 3 × 3. Mun san cewa don nemo matrix mai juyayi, muna buƙatar amfani da aikin =MOBR().
Yanzu mun bayyana yadda ake yin wannan a aikace. Da farko kuna buƙatar zaɓar kewayon G3:I5 (za'a sami matrix mai juzu'i a wurin). Kuna buƙatar nemo abin "Saka Aiki" akan shafin "Formulas".
Za a buɗe maganganun "Saka aikin", inda kake buƙatar zaɓar nau'in "Math". Kuma za a sami aiki a cikin lissafin MOBR. Bayan mun zaɓi shi, muna buƙatar danna maɓallin OK. Na gaba, akwatin maganganu na "Aikin Aiki" ya bayyana, inda muke rubuta kewayon B3: D5, wanda ya dace da matrix A. Ƙarin ayyuka suna kama da canzawa. Kuna buƙatar danna haɗin maɓallin Shift + Ctrl kuma danna Ok.
karshe
Mun bincika wasu misalan yadda zaku iya aiki tare da matrices a cikin Excel, kuma mun bayyana ka'idar. Sai ya zama cewa wannan ba abin tsoro bane kamar yadda ake gani da farko, ko? Yana kawai sauti mara fahimta, amma a zahiri, matsakaicin mai amfani dole ne ya magance matrices kowace rana. Ana iya amfani da su kusan kowane tebur inda akwai ƙaramin adadin bayanai. Kuma yanzu kun san yadda zaku sauƙaƙa rayuwar ku ta yin aiki da su.