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Bir eğitmen, 2x2 matrisin çarpmaya göre tersini bulma yöntemini adım adım göstermektedir.","Videoda, 2x2 matrisin tersinin nasıl hesaplanacağı detaylı olarak anlatılmaktadır. Önce matrisin determinantının nasıl bulunacağı (köşegen elemanları çarpıp çıkarma) gösterilir, ardından ek matrisin nasıl hesaplanacağı (köşegen elemanlarının yerlerinin değiştirilmesi ve eksiliş alınması) açıklanır. Son olarak, determinant ve ek matris kullanılarak ters matrisin nasıl elde edileceği adım adım gösterilir."]},"endTime":124,"title":"2x2 Matrisin Tersini Bulma Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"İki'ye İki Matrisin Çarpmaya Göre Tersinin Bulunması","list":{"type":"unordered","items":["İki'ye iki matrisin çarpmaya göre tersini bulmak sadece iki'ye iki matrislerde mümkündür, daha büyük matrislerde bu işlem zor olur.","İki'ye iki matrisin tersi, bir bölü matrisin determinantı çarpı ek matris formülüyle hesaplanır.","İki'ye iki matris için bu işlem oldukça kolaydır."]},"beginTime":0,"endTime":28,"href":"/video/preview/6766232678988831018?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=0&ask_summarization=1"},{"index":1,"title":"Matrisin Determinantı ve Ek Matrisinin Hesaplanması","list":{"type":"unordered","items":["Matrisin determinantı, köşegen boyunca yapılan işlemle hesaplanır: 3 çarpı 2 eksi eksi 7 çarpı 5.","Ek matrisi bulmak için köşegen üzerindeki elemanların yerleri değiştirilir ve bu elemanların işaretleri değiştirilir.","Matrisin determinantı 6 artı 35, yani 41 olarak hesaplanır."]},"beginTime":28,"endTime":98,"href":"/video/preview/6766232678988831018?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=28&ask_summarization=1"},{"index":2,"title":"Matrisin Çarpmaya Göre Tersinin Son Hali","list":{"type":"unordered","items":["Matrisin çarpmaya göre tersi, bir bölü determinant (1/41) çarpı ek matris ile bulunur.","Sonuç olarak elde edilen matris: 2/41, -5/41, 7/41 ve 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Eğitmen, gelecek videolarda 3x3 matrislerin tersini bulmanın daha eğlenceli olacağını da eklemektedir."]},"endTime":807,"title":"Matrisler ve Ters Matrisler Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Matris Bölmesi ve Birim Matris","list":{"type":"unordered","items":["Matris toplama, çıkarma ve çarpma işlemlerini öğrendikten sonra matris bölmesi konusu ele alınacak.","Matris çarpmasında yön önemlidir, normal çarpmada olduğu gibi a×b=b×a değildir.","Kare matrislerle çarpma her iki yönde yapılabilirken, kare olmayan matrislerle sadece bir yönde yapılabilir."]},"beginTime":0,"endTime":21,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=0&ask_summarization=1"},{"index":1,"title":"Birim Matris","list":{"type":"unordered","items":["Birim matris (I), bir matristir ve büyük I ile gösterilir.","Birim matris herhangi bir matrisle çarpıldığında o matrisi korur, bir matris birim matrisle çarpıldığında da aynı matrisi elde ederiz.","Birim matrisin yapısı, üst sol köşeden sağ alt köşeye uzanan diagonal üzerinde 1'ler, geriye kalan her yerde 0'lar bulunur."]},"beginTime":21,"endTime":134,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=21&ask_summarization=1"},{"index":2,"title":"Birim Matrisin İspatı","list":{"type":"unordered","items":["Birim matrisin bir matrisle çarpıldığında ilk matrisin değişmediği ispatlanabilir.","Birim matrisin bir matrisle çarpılması, ilgili terimleri çarpıp toplamak anlamına gelir.","Birim matrisin bir matrisle çarpılması, o matrisin birinci terim hariç diğer terimlerini sıfırlayarak sadece birinci terimi korur."]},"beginTime":134,"endTime":256,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=134&ask_summarization=1"},{"index":3,"title":"Matris Tersi","list":{"type":"unordered","items":["Normal matematikte 1×a=a ve 1/a×a=1 ilişkisi vardır, buna a'nın tersi denir.","Matris için de benzer bir kavram vardır: Bir matris A ile bir başka matris A⁻¹ çarpıldığında birim matrise eşit olmalıdır.","A×A⁻¹=I ve A⁻¹×A=I olduğundan, A ve A⁻¹ birbirlerinin tersidir."]},"beginTime":256,"endTime":329,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=256&ask_summarization=1"},{"index":4,"title":"Matris Tersinin Hesaplanması","list":{"type":"unordered","items":["2x2 matrisin tersi hesaplaması kolaydır.","3x3 matrisin tersi hesaplaması biraz daha karışıktır.","4x4 matrisin tersi hesaplaması uzun sürebilir ve 5x5 matrisin tersi bulunurken dikkat hatası yapılabilir, bu nedenle bilgisayarın yapması daha uygundur."]},"beginTime":329,"endTime":367,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=329&ask_summarization=1"},{"index":5,"title":"Matrisin Tersinin Hesaplanması","list":{"type":"unordered","items":["Matrisin tersini hesaplamak için öncelikle matrisin determinantı (1/ad-bc) bulunmalıdır.","Matrisin tersi, 1/determinant çarpı yeni matris olarak hesaplanır.","Yeni matrisde sol üstteki eleman ile sağ alttaki eleman yer değiştirir, sol alttaki eleman ile sağ üstteki elemanın işaretleri değiştirilir."]},"beginTime":372,"endTime":441,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=372&ask_summarization=1"},{"index":6,"title":"Determinant Kavramı","list":{"type":"unordered","items":["Determinantın ne olduğunu öğrenmek önemli bir konudur ve ortaokulda hesaplamasını bilmek yeterlidir.","Determinantın işareti |a| şeklinde gösterilir ve a'nın determinantı a=ad-bc formülüyle hesaplanır.","Matrisin tersi, 1/determinant çarpı yeni matris olarak ifade edilir."]},"beginTime":441,"endTime":504,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=441&ask_summarization=1"},{"index":7,"title":"Örnek Problemin Çözümü","list":{"type":"unordered","items":["B matrisi {3 -4; 2 -5} olarak verildiğinde, B'nin determinantı 3(-5)-2(-4)=-15+8=-7 olarak hesaplanır.","B'nin tersi, -1/7 çarpı yeni matris olarak bulunur: {-5/7 4/7; -2/7 3/7}.","B'nin tersi ile B'nin çarpımı birim matrisi verir, bu da B'nin tersinin doğru olduğunu doğrular."]},"beginTime":504,"endTime":792,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=504&ask_summarization=1"},{"index":8,"title":"Sonuç","list":{"type":"unordered","items":["İki elemanlı matrisin tersi böyle bulunur.","Gelecek videoda üç elemanlı matrisin tersini bulmak daha eğlenceli olacak."]},"beginTime":792,"endTime":801,"href":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=792&ask_summarization=1"}],"linkTemplate":"/video/preview/14439369815550624254?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Ters Matrisler (Kalkülüs / Matrisler)","related_orig_text":"MasterMind Tech (E2MATRIX)","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"MasterMind Tech 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İçerik üreticisi, 60 kilowattlık bir şarj cihazından yaklaşık 1,5 saat süren şarj sürecini, şarj hızlarını ve batarya doluluğunu adım adım anlatıyor. Ayrıca, batarya sağlığını korumak için şarjın yüzde 20-80 aralığında tamamlanması gerektiği ve yüzde 100'e kadar şarj edilmesinin zaman açısından faydalı olmayacağı bilgisi paylaşılıyor. Video sonunda, batarya kapasitesinin gerçek değerinin 65 kilowatt civarında olduğu ve yüzde sıfırdan sonra da yaklaşık 15-20 kilometre yol yapılabildiği belirtiliyor."]},"endTime":380,"title":"Elektrikli Araç Şarj Testi","beginTime":0}],"fullResult":[{"index":0,"title":"Elektrikli Araç Yolculuğu ve Şarj Durumu","list":{"type":"unordered","items":["Yüzde elli şarjda çıkan araç, yüzdoksanüç kilometre yol yapmış ve ortalama ondörtvirgülyirmi kilowatt tüketim sağlamış.","Köy yolları ve inişli çıkışlı yollarda ortalama tüketim altmışbir kilometre, yaklaşık yüz-yüzyirmi kilometresi yüzle, diğer yollarda elli-altmış kilometre hızlarla gidilmiş.","Araç şarjı yüzde bir menzil vermiyor ve DC istasyonundan şarj işlemi başlatılıyor."]},"beginTime":0,"endTime":77,"href":"/video/preview/3558686529880332797?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=0&ask_summarization=1"},{"index":1,"title":"Şarj Süreci ve Verileri","list":{"type":"unordered","items":["Şarj işlemi yaklaşık bir buçuk saat sürmüş, saat 57'de başlayıp 12:26'da sonuçlanmış.","Şarj başlangıcında yüzde bir'e taktığımızda araç ellidokuz kilowatt gibi bir şarj hızıyla başlamış, sonra yüzde kırkyedi'ye gelmiş.","Saat 11:46'ya geldiğinde şarj hızı kırkiki kilovata düşmüş, batarya doluluğu yüzde yetmiş beşe gelmiş."]},"beginTime":77,"endTime":187,"href":"/video/preview/3558686529880332797?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=77&ask_summarization=1"},{"index":2,"title":"Şarj Hızı ve Batarya Sağlığı","list":{"type":"unordered","items":["Batarya doluluğu yüzde seksen'e geldiğinde \"batarya sağlığını korumak için aracınızı şarjdan çıkarın\" uyarısı gelmiş.","Bataryayı yüzde seksen'e kadar doldurmanın iki sebebi: batarya sağlığını korumak ve şarj hızının yavaşladığı için zaman anlamında fayda sağlamaması.","Yüzde seksen'den yüzde yüze dolumu iki-üç şarjlarla tamamlamak daha iyi olacaktır."]},"beginTime":187,"endTime":270,"href":"/video/preview/3558686529880332797?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=187&ask_summarization=1"},{"index":3,"title":"Şarj Hızının Düşüşü ve Batarya Kapasitesi","list":{"type":"unordered","items":["Yüzde doksaniki'de şarj hızı yirmiiki k'ya düşmüş, yüzde doksanbeş'e geldiğinde ondört k'ya, yüzde doksansekiz'de on k'ya, yüzde doksandokuz'da yedivirgülotuz k'ya, yüzde yüz'e geldiğinde altıvirgülon k'ya düşmüş.","Batarya doluluğu yüzde yüze geldiğinde altmışikivirgülyetmiş kilowatt enerji alınmış, batarya kapasitesi bize altmış kilowatt olarak söylenmiş.","Batarya kapasitesi gerçekte altmışbeş kilowatt'a yakın bir değer, yüzde sıfırdan sonra da yol yapılabilir ancak batarya sağlığı açısından istenilen değerler değil."]},"beginTime":270,"endTime":373,"href":"/video/preview/3558686529880332797?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=270&ask_summarization=1"}],"linkTemplate":"/video/preview/3558686529880332797?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Megane E-Tech Gerçek Batarya Kapasitesi - 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İki matrisin eşit olması için büyüklüklerinin aynı olması ve her bileşeninin karşılıklı olarak eşit olması gerektiği belirtilmektedir. Eğitmen, bu kavramı iki farklı örnek üzerinden pekiştirmektedir. İlk örnekte trigonometrik fonksiyonlar kullanılarak matris eşitliği çözülmekte, ikinci örnekte ise mutlak değerli denklemler içeren bir matris eşitliği problemi ele alınmaktadır."]},"endTime":449,"title":"İki Matrisin Eşitliği Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"İki Matrisin Eşitliği Kavramı","list":{"type":"unordered","items":["İki matrisin eşitliğinden bahsedebilmek için matrislerin büyüklükleri (boyutları veya tipleri) aynı olmalıdır.","İki matrisin eşit olması için gerek ve yeter koşul, tüm bileşenlerin (girdilerin) karşılıklı olarak eşit olmasıdır.","Matrislerin eşit olması durumunda, karşılıklı girdilerin değerleri birbirine eşit olmalıdır."]},"beginTime":1,"endTime":83,"href":"/video/preview/15878464392709229722?parent-reqid=1769574102872831-13493023202866891256-balancer-l7leveler-kubr-yp-vla-222-BAL&text=MasterMind+Tech+%28E2MATRIX%29&t=1&ask_summarization=1"},{"index":1,"title":"Matris Eşitliği Örnekleri","list":{"type":"unordered","items":["Matris 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