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İç açıortay teoremi, bir üçgenin bir açısını tam ortadan kesen ve açının ölçüsünü ikiye bölen bir kesenin özellikleri üzerine kurulmuştur. Konuşmacı, teoremin ispatını kelebek benzerliği kullanarak göstermekte ve bu teoremin içte çember ve içte çemberle ilgili magel noktası gibi önemli noktalar ve teoremler için temel oluşturduğunu vurgulamaktadır."]},"endTime":249,"title":"Liseler İçin Geometri: İç Açıortay Teoremi","beginTime":0}],"fullResult":[{"index":0,"title":"İç Açıortay Teoremi'nin Önemi","list":{"type":"unordered","items":["İç açıortay teoremi, düzlem geometrisinde içte çember ve magel noktası gibi önemli noktalar ve teoremler için temel oluşturur.","Düzlem geometrisine ilgi verenler ve bu alanda gelişmek isteyenler için iç açıortay teoremini ve uygulamalarını bilmek şiddetle önerilir."]},"beginTime":1,"endTime":36,"href":"/video/preview/3992927333572215249?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=1&ask_summarization=1"},{"index":1,"title":"İç Açıortay Kavramı","list":{"type":"unordered","items":["İç açıortay, üçgenin bir açısını tam ortadan, açının ölçüsünü ikiye bölen ve açının simetri merkezi olan bir kesen olarak tanımlanır.","İç açıortay, açıyı iki eş ölçüye ayıran bir kesen olup, bu iki eş açı oluşur."]},"beginTime":36,"endTime":92,"href":"/video/preview/3992927333572215249?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=36&ask_summarization=1"},{"index":2,"title":"İç Açıortay Teoremi","list":{"type":"unordered","items":["İç açıortay teoremine göre, çaprazların çarpımı birbirine eşittir: a×k = b×p veya a×b = p×k.","Teoremin ispatını yapabilmek için benzerlik ve kelebek benzerliği bilgisi gereklidir."]},"beginTime":92,"endTime":110,"href":"/video/preview/3992927333572215249?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=92&ask_summarization=1"},{"index":3,"title":"Teoremin İspatı","list":{"type":"unordered","items":["BA doğru parçasına paralel bir doğru parçası 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Eğitmen önce determinantın tanımını, kofaktör açılımını ve permütasyonları hatırlatmakta, ardından lineer denklem sistemlerinin çözümlerini matrisler üzerinden açıklamaktadır. Cramer kuralının temel prensibi, katsayılar matrisinin tersinin determinantının çarpımına eşit olduğu teoremi kullanılarak, lineer denklem sistemlerinin çözümlerinin nasıl bulunabileceği gösterilmektedir.","Eğitmen, Cramer metodunun katsayılar matrisinin determinantı sıfırdan farklı olan lineer denklem sistemlerinde spesifik bir x değerini bulmak için kullanıldığını belirtmekte ve büyük matrislerde işe yaramadığını ancak spesifik bir x değerini bulmak için çok kuvvetli olduğunu vurgulamaktadır. Video, Cramer metodu ve uygulaması ile ilgili soru çözüleceği bilgisiyle sonlanmaktadır."]},"endTime":1034,"title":"Lineer Cebirde Cramer Kuralı Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Lineer Cebirde Gramer Kuralı","list":{"type":"unordered","items":["Video, özellikle üniversite öğrencileri ve öğretmenlik okuyanlar için önemli olan lineer cebirde gramer kuralını ele alıyor.","Gramer kuralını anlamak için kofaktör açılımı, determinant tanımı, permütasyonlar ve inversiyonlar konularını bilmek gerekiyor.","Gramer kuralı, lineer denklem sistemlerinin çözümlerini bulmak için kullanılan bir yöntemdir."]},"beginTime":0,"endTime":52,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=0&ask_summarization=1"},{"index":1,"title":"Lineer Denklem Sistemi ve Katsayılar Matrisi","list":{"type":"unordered","items":["Lineer denklem sistemi, n bilinmeyenli bir denklem sistemi olarak tanımlanıyor.","Sistemin katsayılar matrisi A olarak adlandırılıyor ve kare matris haline getiriliyor.","Matrisin determinantı sıfırdan farklı olmalı, aksi takdirde denklem sistemi dinamik olur."]},"beginTime":52,"endTime":133,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=52&ask_summarization=1"},{"index":2,"title":"Lineer Denklem Sisteminin Çözümü","list":{"type":"unordered","items":["Lineer denklem sisteminin çözümü A×x = b şeklinde ifade ediliyor.","A terslenebilirse, denklem A⁻¹×b = x şeklinde yazılabilir.","B matrisi, denklem sisteminin sağ tarafındaki değerlerden oluşan n×1 tipinde bir sütun matrisidir."]},"beginTime":133,"endTime":216,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=133&ask_summarization=1"},{"index":3,"title":"A'nın Tersi ve A'nın Adjoint'i","list":{"type":"unordered","items":["Lineer cebirde A matrisinin adjoint'i (adj A) öğrenilir ve bu konu gramer kuralında kullanılır.","A'nın tersini bulmak için A'nın determinantının çarpmaya göre tersinin A'nın adjoint ile skaler çarpımı kullanılır.","Bu yöntem maliyetli olabilir çünkü adjoint bulmak için tüm kofaktörleri hesaplamak gerekir ve büyük boyutlu matrisler için bu işlem zordur."]},"beginTime":216,"endTime":332,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=216&ask_summarization=1"},{"index":4,"title":"Cramer Kuralının İspatı","list":{"type":"unordered","items":["Cramer kuralı, lineer denklem sisteminin çözümlerini bulmak için A'nın adjoint'i kullanılır.","A'nın adjoint'i, kofaktör açılımı bölü determinant A şeklinde tanımlanır.","A'nın tersi yerine A'nın adjoint'i kullanılarak x = D×B şeklinde bir denklem elde edilir."]},"beginTime":332,"endTime":550,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=332&ask_summarization=1"},{"index":5,"title":"Cramer Kuralının Sonuçlanması","list":{"type":"unordered","items":["Matris çarpımı sonucunda x = (a₁₁/det A)×b₁ + (a₂₁/det A)×b₂ + ... + (aₙ₁/det A)×bₙ şeklinde bir denklem elde edilir.","Bu denklemde x₁, x₂, ..., xₙ değerleri sırasıyla a₁₁/det A, a₂₁/det A, ..., aₙ₁/det A ile b₁, b₂, ..., bₙ değerlerinin çarpımlarının toplamıdır.","Her tarafa determinant A ile çarpıldığında determinant A×x₁ = a₁b₁ + a₂b₂ + ... + aₙbₙ şeklinde bir denklem elde edilir."]},"beginTime":550,"endTime":731,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=550&ask_summarization=1"},{"index":6,"title":"Cramer Metodu ve DJ Matrisi","list":{"type":"unordered","items":["DJ matrisi, A matrisinin bir j'nin sütun silinmiş hali olup, j'nin yerine B matrisinin b'inci sütunu konulmuştur.","DJ matrisinin determinantı, j'nin sütuna göre kofaktör açılımı ile hesaplanabilir ve bu açılım A matrisinin determinantı ile benzerlik gösterir.","Cramer metodu, lineer denklem sisteminde katsayılar matrisinin determinantı sıfırdan farklıysa uygulanabilir ve istenen x değerini bulmak için kullanılır."]},"beginTime":734,"endTime":977,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=734&ask_summarization=1"},{"index":7,"title":"Cramer Metodunun Kullanım Alanları","list":{"type":"unordered","items":["Cramer metodu büyük matrislerde işe yaramaz, ancak spesifik olarak tek bir x değerini bulmak istendiğinde çok kuvvetlidir.","Cramer metodu, A matrisinin determinantı ile DJ matrisinin determinantı arasındaki oranla x değerini bulmayı sağlar."]},"beginTime":977,"endTime":1028,"href":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=977&ask_summarization=1"}],"linkTemplate":"/video/preview/15071248521290452715?parent-reqid=1765295601272259-2914976152379181968-balancer-l7leveler-kubr-yp-sas-159-BAL&text=Euler%27in+Masas%C4%B1&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Lineer Cebir Serisi: Cramer Metodu & İspat","related_orig_text":"Euler'in Masası","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Euler\\u0027in 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