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Eğitmen, iki farklı küme örneği üzerinden bu kuralları uygulamalı olarak göstermekte ve ilk kümenin subspace olmadığını, ikinci kümenin ise subspace olduğunu kanıtlamaktadır."]},"endTime":411,"title":"Lineer Cebir Dersinde Subspace Kavramı","beginTime":0}],"fullResult":[{"index":0,"title":"Subspace Tanımı ve İlk Örnek","list":{"type":"unordered","items":["W, R² kümesinin elemanları olan (x₁, x₂, x₁x₂) şeklinde tanımlanan bir alt kümesidir.","Subspace olmanın iki kuralı vardır: herhangi iki vektörün toplamı ve herhangi bir vektörün sabit bir sayı ile çarpımı da W kümesinde olmalıdır.","İlk örnekte, (x₁+y₁, x₂+y₂, x₁x₂+xy₁y₂) toplamı W kümesinin elemanı değildir çünkü (x₁+y₁)(x₂+y₂) ifadesi sadece x₁x₂+xy₁y₂'e eşit değildir."]},"beginTime":0,"endTime":258,"href":"/video/preview/18159469782597565365?parent-reqid=1769546609591570-7699331028436575351-balancer-l7leveler-kubr-yp-vla-92-BAL&text=Elite+Astro+Subspace&t=0&ask_summarization=1"},{"index":1,"title":"İkinci Örnek ve Sonuç","list":{"type":"unordered","items":["İkinci örnekte, (a, b, a+2b) şeklinde tanımlanan bir alt küme incelenmektedir.","Bu örnekte, (a₁+a₂, b₁+b₂, a₁+a₂+2b₁+2b₂) toplamı W kümesinin elemanıdır çünkü (a₁+a₂)(b₁+b₂) ifadesi sadece a₁+a₂+2b₁+2b₂'e eşittir.","Ayrıca, alfa(a, b, a+2b) ifadesi de W kümesinin elemanıdır çünkü alfa(a₁, b₁, a₁+2b₁) ifadesi sadece alfa(a₁), alfa(b₁), alfa(a₁+2b₁) olarak yazılabilir."]},"beginTime":258,"endTime":397,"href":"/video/preview/18159469782597565365?parent-reqid=1769546609591570-7699331028436575351-balancer-l7leveler-kubr-yp-vla-92-BAL&text=Elite+Astro+Subspace&t=258&ask_summarization=1"}],"linkTemplate":"/video/preview/18159469782597565365?parent-reqid=1769546609591570-7699331028436575351-balancer-l7leveler-kubr-yp-vla-92-BAL&text=Elite+Astro+Subspace&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Lineer Cebir - Alt uzay - Subspace - Örnek Soru Çözümü - 2","related_orig_text":"Elite Astro 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Hocaya soru sorabileceğiniz canlı yayınlarımız hakkında bilgi edinmek için: https://www.aceleders.com/canliyayin...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2432659/79f285ddf0aebbb6384d646bd7af6ec7/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/FB36534DA964A8E7FC6AA29FE26CEE2987D6DF53A5FB4F6F794AD0AA893793731CDFB135D8ED281B178C387760409B8D9D8A158B9F5FA0A743C6D836B4358B7B.mp4","videoType":"video/mp4"},"target":"_self","position":"17","reqid":"1769546609591570-7699331028436575351-balancer-l7leveler-kubr-yp-vla-92-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769546609591570-7699331028436575351-balancer-l7leveler-kubr-yp-vla-92-BAL&text=videoid:17249658250127735070","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik dersinde eğitmen tarafından sunulan bir ders anlatımıdır.","Videoda, bir vektör uzayının alt uzayını (subspace) bulma konusu ele alınmaktadır. Eğitmen, önce bir vektör uzayının elemanlarını belirleyip, ardından bu elemanların toplamını hesaplamaktadır. Son olarak, bu toplamın da aynı vektör uzayının elemanı olduğunu göstererek, bu vektör uzayının alt uzay olduğunu kanıtlamaktadır. Video, matematiksel hesaplamalar ve vektör uzayları konusunu öğrenmek isteyenler için faydalı olabilir."]},"endTime":129,"title":"Matematik Dersinde Subspace Kavramı","beginTime":0}],"fullResult":[{"index":0,"title":"Vektörlerin Toplanması","list":{"type":"unordered","items":["İki vektör v₁ ve v₂ tanımlanıyor: v₁ = a₁, 2a₁, 3a₁ ve v₂ = 0, 2a₂, 3a₂.","v₁ ve v₂ vektörleri toplandığında, sonuç v₁ + v₂ = a₁, 2a₁, 2a₁ + 2a₂, 3a₁ + 3a₂ şeklinde elde ediliyor.","Bu sonuç, davulun elemanı olarak kabul ediliyor çünkü davulun elemanları birinci elemanı, bir sıfır, birincinin iki katı ve birincinin üç katı şeklinde yazılır."]},"beginTime":15,"endTime":93,"href":"/video/preview/17249658250127735070?parent-reqid=1769546609591570-7699331028436575351-balancer-l7leveler-kubr-yp-vla-92-BAL&text=Elite+Astro+Subspace&t=15&ask_summarization=1"},{"index":1,"title":"Vektörün Katsayı ile Çarpılması","list":{"type":"unordered","items":["v₁ vektörü alfa katsayısı ile çarpılıyor: alfa·v₁ = alfa·a₁, 0, 2alfa·a₁, 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