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Hazırlayan: Kemal Duran (Matematik Öğretmeni)...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2968351/d78706d1d3b142eecdeb98d896edc06c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/W_vnMAAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1769773867733075-10212794921562648685-balancer-l7leveler-kubr-yp-klg-59-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769773867733075-10212794921562648685-balancer-l7leveler-kubr-yp-klg-59-BAL&text=videoid:11714511211057843996","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik dersi formatındadır.","Video, matrislerde boş uzay (null space) ve boyutu (nullity) kavramlarını detaylı şekilde ele almaktadır. Eğitmen önce teorik bilgileri anlatıp, ardından bir örnek matris üzerinden genişletilmiş katsayılar matrisi oluşturma, eşeron forma getirme, temel-serbest değişkenleri belirleme ve boşuzayın çözüm elemanlarını bulma işlemlerini adım adım göstermektedir.","Videoda ayrıca rank ve nullity kavramları arasındaki ilişki de açıklanmakta ve matrislerde boşuzay bulma işleminin temel adımları özetlenmektedir. Bu içerik, matrislerde boşuzay kavramını öğrenmek isteyenler için kapsamlı bir rehber niteliğindedir."]},"endTime":1607,"title":"Matrislerde Boş Uzay ve Boyutu Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Boş Uzay ve Boyutu","list":{"type":"unordered","items":["Boş uzay (null space) bir matrisin x gibi bir sütun matrisi ile çarpıldığında sonucun sıfıra eşitlenmesiyle ortaya çıkan denklemin çözümleri kümesidir.","Boş uzayın boyutu (nullity) ise bu çözüm kümesinin kaç elemanlı olduğu ile ilgilidir.","Boş uzayın bulunuşu, bir matrisin x sütun matrisi ile çarpılıp sonucun sıfıra eşitlenmesi ile ortaya çıkan denklemin çözümleridir."]},"beginTime":1,"endTime":112,"href":"/video/preview/11714511211057843996?parent-reqid=1769773867733075-10212794921562648685-balancer-l7leveler-kubr-yp-klg-59-BAL&text=Null_Experis&t=1&ask_summarization=1"},{"index":1,"title":"Örnek Problemin Çözümü","list":{"type":"unordered","items":["Örnek problemde verilen 4x6 boyutlu matrisin boş uzayını ve boyutunu bulmak için matrisi x sütun matrisi ile çarpıp sonucu sıfıra eşitlemek gerekir.","Matrisin sütun sayısı bilinmeyen sayısını gösterdiğinden, 6 sütun olduğu için x sütun matrisi 6 bilinmeyen içermelidir.","Çözüm için genişletilmiş katsayılar matrisi oluşturulup eşelon forma getirilmesi gerekir."]},"beginTime":112,"endTime":347,"href":"/video/preview/11714511211057843996?parent-reqid=1769773867733075-10212794921562648685-balancer-l7leveler-kubr-yp-klg-59-BAL&text=Null_Experis&t=112&ask_summarization=1"},{"index":2,"title":"Eşelon Forma Getirme ve Çözüm","list":{"type":"unordered","items":["Eşelon forma getirirken ilk satırın ilk elemanı bir yapılmalı ve alt tarafı sıfırlanmalıdır.","İlk pivot bulununca, ikinci pivot çaprazında aranır ve altı sıfırlanır.","Üçüncü pivot için çaprazda bir elde etmek mümkün değilse, başka pivot olmadığı 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bulunur.","Pivot bulunan sütunlar temel değişkenler, diğerleri serbest değişkenlerdir.","Serbest değişkenlere harfler atanır ve temel değişkenler bu harfler cinsinden ifade edilir."]},"beginTime":949,"endTime":1096,"href":"/video/preview/11714511211057843996?parent-reqid=1769773867733075-10212794921562648685-balancer-l7leveler-kubr-yp-klg-59-BAL&text=Null_Experis&t=949&ask_summarization=1"},{"index":5,"title":"Boş Uzayın Çözümü","list":{"type":"unordered","items":["Boş uzayın çözümü, temel değişkenlerin serbest değişkenler cinsinden ifade edilmesiyle elde edilir.","Çözüm elemanları parantez içinde toplanarak boş uzayın bazının elemanları oluşturulur.","Boş uzayın boyutu, bazının eleman sayısıdır ve İngilizce'de \"nullity\" olarak adlandırılır."]},"beginTime":1096,"endTime":1351,"href":"/video/preview/11714511211057843996?parent-reqid=1769773867733075-10212794921562648685-balancer-l7leveler-kubr-yp-klg-59-BAL&text=Null_Experis&t=1096&ask_summarization=1"},{"index":6,"title":"Rank ve 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