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Řekneme si, co je to lineální obal vektorů, a ukážeme si alternativní metody řešení soustav rovnic, jako je například Cramerovo pravidlo.\n\n- **Opakování analytické geometrie:**\n  - Přehled základních principů analytické geometrie\n\n- **Vektorové prostory:**\n  - Definice vektorového prostoru a jeho vlastnosti\n  - Rozlišení toho, co je a není vektorový prostor\n\n- **Soustavy lineárních rovnic:**\n  - Úvod do soustav lineárních rovnic\n  - Gaussova eliminační metoda – princip a detailní postup\n  - Geometrická interpretace řešení soustav rovnic\n  - Příklady na soustavy s jedním řešením, žádným řešením i nekonečně mnoha řešeními\n  - Speciální případy soustav a soustavy s parametry\n\n- **Lineární závislost a nezávislost vektorů:**\n  - Intuitivní vysvětlení a definice pojmů\n  - Odvození metody pro zjišťování lineární závislosti a nezávislosti\n  - Praktické příklady, včetně případů s parametry\n\n- **Lineární kombinace vektorů:**\n  - Jak vyjádřit vektor jako lineární kombinaci jiných vektorů\n\n- **Báze, lineární obal a generátory:**\n  - Co jsou báze, lineární obal a generátory vektorového prostoru\n  - Procvičení a příklady na pochopení těchto pojmů\n\n- **Alternativní metody řešení soustav rovnic:**\n  - Cramerovo pravidlo\n  - Řešení soustav rovnic pomocí inverzní matice\n\n- **Bonusové téma:**\n  - Řešení těžké soustavy lineárních rovnic 3x3 s parametrem.\n\n\n## **Pro koho je kurz určený?**\n\nKurz je primárně určený pro **studenty vysokých škol**, ale může se hodit i pokročilým středoškolákům.","Vysokoškolská lineární algebra. 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ušetříme ti nervy i peníze","\u002Fvideokurz\u002Fbalicek-prijimaci-zkousky-na-stredni",{"id":8171,"width":1991,"height":1992},"05fc8257-bdaa-49a7-a489-b65fa9ed4837",4960,{"duration":8174,"lections":2019,"tests":1085,"testsQuestions":8175,"rating":1024,"packageCoursesMaxPrice":8172,"packageCoursesTotalPricesPerLicenceLength":8176,"packageCourses":91,"minPeriodForRating":8179},114855,516,{"365":8172,"730":8177,"-1":8178},5750,9920,9188400000,[8181,8188,8195],{"id":757,"name":8182,"slug":8183,"description_mini":8184,"type":392,"url":8185,"previewImage":8186},"Přijímačky na SŠ z 9. třídy (4leté obory) - ČEŠTINA","prijimacky-na-stredni-skoly-4lete-obory-cestina","Příprava na státní přijímací zkoušky na gymnázia a střední školy (4leté obory) - ČESKÝ JAZYK","\u002Fvideokurz\u002Fprijimacky-na-stredni-skoly-4lete-obory-cestina",{"id":8187,"width":1991,"height":1992},"e279de6e-f56f-48fc-bd40-75cc6393c2fd",{"id":905,"name":8189,"slug":8190,"description_mini":8191,"type":392,"url":8192,"previewImage":8193},"Přijímačky nanečisto na SŠ z 9. třídy (4leté obory) - ČEŠTINA","prijimacky-nanecisto-z-cestiny","Zkuste složit cvičný přijímačkový test z českého jazyka v pohodlí domova.","\u002Fvideokurz\u002Fprijimacky-nanecisto-z-cestiny",{"id":8194,"width":1991,"height":1992},"327ddcf1-0826-4166-95b6-322a50c83a03",{"id":867,"name":8196,"slug":8197,"description_mini":8198,"type":392,"url":8199,"previewImage":8200},"Přijímačky nanečisto na SŠ z 9. třídy (4leté obory) - MATIKA","prijimacky-nanecisto-z-matiky","Vyzkoušej si přijímačky z matematiky v pohodlí domova.","\u002Fvideokurz\u002Fprijimacky-nanecisto-z-matiky",{"id":8201,"width":1991,"height":1992},"f1580704-288a-4e25-a577-65688aee824b",[8203],{"id":5,"name":6,"surname":7,"biography":8,"web":9,"slug":10},[8205,8206,8209,8210],{"id":164,"name":1033,"slug":1034},{"id":280,"name":8207,"slug":8208},"Základní škola","zakladni-skola",{"id":114,"name":407,"slug":408},{"id":13,"name":413,"slug":414},"\u002Fvideokurz\u002Fprijimacky-na-stredni-skoly-4lete-obory-matematika",{"duration":8213,"lections":867,"tests":526,"testsQuestions":6403,"rating":8214,"packageCoursesMaxPrice":25,"packageCoursesTotalPricesPerLicenceLength":8215,"packageCourses":25,"minPeriodForRating":8216},48201,95,{},3856080000,[],"2019-03-21T00:00:00.000Z",{"id":775,"name":8166,"slug":8167,"previewImage":8220,"description":8221,"description_mini":8168,"price":2513,"priceVariants":8222,"structure":8228,"type":2509,"introductionVideo":48,"packageCourses":8229,"coursePackages":8238,"relatedCourses":8239,"authors":8240,"categories":8248,"url":8169,"isFree":416,"counts":8256,"variant_title":8258,"variant_description":8259,"variants":8260,"status":50,"date_published":8218},{"id":8171,"width":1991,"height":1992},"Tento zvýhodněný balíček ti pomůže zvládnout **jednotnou (státní) přijímací zkoušku (JPZ)** na střední školy a gymnázia (**4leté obory**). Obsahem jsou **4 navazující videokurzy**. V nich se naučíš vše, co k přijímačkám musíš umět. Navíc si i nanečisto napíšeš cvičné testy věrně simulující ostrou zkoušku, která tě v dubnu čeká.\n\n- dva rozsáhlé kurzy, které jsme připravili s našimi nejlepšími lektory na **češtinu** (**[Mgr. Tomáš Ficza](\u002Flektor\u002Ftomas-ficza \"Profil lektora Mgr. Tomáš Ficza\")**) a **matematiku** (**[Marek Valášek](\u002Flektor\u002Fmarek-valasek \"Profil lektora Marek Valášek\")**),\n- a k tomu dva kurzy **přijímaček nanečisto** – **z češtiny** a **z matematiky** – kde si vyzkoušíš reálné testy se vším všudy:\n\t- pokyny jako u ostré zkoušky\n    - časový limit\n    - zadání a záznamový arch\n    - a hlavně podrobná oprava a vyhodnocení s lektorem\n\nČeká na tebe **detailní vysvětlení veškerého učiva**, která tě může u přijímaček potkat – a zároveň možnost ověřit si, **jak na tom skutečně jsi**, kde ztrácíš body a co dohnat. Tak, aby tě u ostrého termínu nic nepřekvapilo.\n\nVideokurzy obsahují strukturovaně rozdělenou **veškerou látku**, spoustu **příkladů na procvičení** i doplňkové materiály.\n\nAž budeš mít látku v ruce, **přejdeš na přijímačky nanečisto** – získáš jistotu, tempo i klid v hlavě, protože už budeš přesně vědět, co tě u ostrých přijímaček čeká.\n\nDíky části videí zdarma si navíc můžeš dopředu vyzkoušet, jak ti bude vyhovovat učitel a jeho styl výkladu.",[8223,8224,8227],{"id":1175,"sort_order":25,"course_id":775,"licence_length":29,"licence_length_label":30,"price_ratio":13,"price":2513},{"id":1184,"sort_order":13,"course_id":775,"licence_length":35,"licence_length_label":36,"price_ratio":8225,"price":8226},1.15,3440,{"id":3782,"sort_order":41,"course_id":775,"licence_length":42,"licence_length_label":43,"price_ratio":5,"price":5631},[],[8230,8232,8234,8236],{"id":757,"name":8182,"slug":8183,"description_mini":8184,"type":392,"url":8185,"previewImage":8231},{"id":8187,"width":1991,"height":1992},{"id":766,"name":7431,"slug":7432,"description_mini":7436,"type":392,"url":8211,"previewImage":8233},{"id":7434,"width":1991,"height":1992},{"id":905,"name":8189,"slug":8190,"description_mini":8191,"type":392,"url":8192,"previewImage":8235},{"id":8194,"width":1991,"height":1992},{"id":867,"name":8196,"slug":8197,"description_mini":8198,"type":392,"url":8199,"previewImage":8237},{"id":8201,"width":1991,"height":1992},[],[],[8241,8247],{"id":4121,"name":8242,"surname":8243,"biography":8244,"web":8245,"slug":8246},"Tomáš","Ficza","> Lektor češtiny, literatury a angličtiny\n\nUčení je jedním z Tomášových velkých koníčků, mezi ty další patří sport, literatura, divadlo, dobré jídlo a víno.\n\nTomáš vyučuje na gymnáziu **český a anglický jazyk** a také **dramatickou výchovu**. Dříve přednášel na Pedagogické fakultě Univerzity Karlovy (předmět Moderní angličtina) a hrál anglické divadlo v divadelním spolku Drama Queens. Dnes se kromě výuky a videokurzů soustředí také na školení učitelů.\n\nTomáš je **vyškolený hodnotitel písemných maturitních prací a zkoušející u maturit** z výše zmíněných předmětů, také certifikovaný hodnotitel **PET**, **FCE** a **CAE** zkoušek. Tomáš říká: \"*LearnTube je pro mě možnost, jak se podělit o své největší zájmy a zároveň pomoci studentům k úspěšnému zvládnutí jejich cílů.*\"\n\nPokud byste potřebovali osobní konzultaci, opravu slohové práce nebo byste se chtěli domluvit na doučování, můžete mu napsat na tomasficza@gmail.com. Toto jsou placené služby nad rámec videokurzů.","","tomas-ficza",{"id":5,"name":6,"surname":7,"biography":8,"web":9,"slug":10},[8249,8250,8251,8252,8255],{"id":164,"name":1033,"slug":1034},{"id":280,"name":8207,"slug":8208},{"id":114,"name":407,"slug":408},{"id":123,"name":8253,"slug":8254},"Čeština","cestina",{"id":13,"name":413,"slug":414},{"duration":8174,"lections":2019,"tests":1085,"testsQuestions":8175,"rating":1024,"packageCoursesMaxPrice":8172,"packageCoursesTotalPricesPerLicenceLength":8257,"packageCourses":91,"minPeriodForRating":8179},{"365":8172,"730":8177,"-1":8178},"Kompletní příprava LearnTube","Dostaneš naši kompletní přípravu na přijímačky. Zkrátka vše, co vidíš v tomto balíčku.\n- **266** lekcí\n- **516** procvičování\n- **31+** hodin videí",[8261],{"id":975,"url":8262,"priceVariants":8263,"variant_title":8271,"variant_description":8272},"\u002Fvideokurz\u002Fbalicek-prijimaci-zkousky-na-stredni-techambition",[8264,8266,8268],{"id":1386,"sort_order":13,"course_id":975,"licence_length":29,"licence_length_label":30,"price_ratio":13,"price":8265},5990,{"id":1395,"sort_order":5,"course_id":975,"licence_length":35,"licence_length_label":36,"price_ratio":2002,"price":8267},6590,{"id":4108,"sort_order":41,"course_id":975,"licence_length":42,"licence_length_label":43,"price_ratio":8269,"price":8270},1.5,8990,"Příprava LearnTube + aplikace Techambition","Dostaneš naši kompletní přípravu na přijímačky a ještě navíc chytré procvičování od firmy **Techambition**. S touto kombinací si můžeš být prakticky jistý, že to zvládneš.\n\n- **266** lekcí\n- **516** procvičování\n- **31+** hodin videí\n- **Tisíce úloh navíc s inteligentní nápovědou**\n- **Procvičování geometrických úloh**",{"id":4463,"name":5576,"slug":5577,"previewImage":8274,"description":8275,"description_mini":5578,"price":5582,"priceVariants":8276,"structure":8285,"type":2509,"introductionVideo":48,"packageCourses":8286,"coursePackages":8291,"relatedCourses":8292,"authors":8293,"categories":8296,"url":5579,"isFree":416,"counts":8304,"variant_title":48,"variant_description":48,"variants":8306,"status":50,"date_published":8307},{"id":5581,"width":1991,"height":1992},"**Scio testy jsou nezávislé a spravedlivé zkoušky**, kterými na desítkách vysokých škol nahrazují standardní přijímačky. Jejich výsledek pak rozhoduje o tom, jestli se vám na danou školu podaří dostat nebo ne.\n\nObsahem tohoto zvýhodněného balíčku jsou **dva video kurzy**, které vás odborně připraví na **Scio testy OSP** (OSP = obecné studijní předpoklady). Získáte díky nim všechny znalosti potřebné k úspěšnému absolvování Scio testů.\n\nVašimi průvodci přípravou na Scio bude **[Mgr. Tomáš Ficza](https:\u002F\u002Flearntube.cz\u002F?page=channel&a=19 \"Profil lektora Mgr. Tomáš Ficza\")**, náš nejlepší učitel českého jazyka, a **[Marek Valášek](https:\u002F\u002Flearntube.cz\u002F?page=channel&a=3 \"Profil lektora Marek Valášek\")**, slavný internetový učitel matematiky.",[8277,8279,8283],{"id":8278,"sort_order":25,"course_id":4463,"licence_length":29,"licence_length_label":30,"price_ratio":13,"price":5582},126,{"id":8280,"sort_order":13,"course_id":4463,"licence_length":35,"licence_length_label":36,"price_ratio":8281,"price":8282},127,1.4,2090,{"id":4171,"sort_order":41,"course_id":4463,"licence_length":42,"licence_length_label":43,"price_ratio":5,"price":8284},2980,[],[8287,8289],{"id":616,"name":5064,"slug":5065,"description_mini":5069,"type":392,"url":5609,"previewImage":8288},{"id":5067,"width":1991,"height":1992},{"id":697,"name":5593,"slug":5594,"description_mini":5069,"type":392,"url":5595,"previewImage":8290},{"id":5597,"width":1991,"height":1992},[],[],[8294,8295],{"id":4121,"name":8242,"surname":8243,"biography":8244,"web":8245,"slug":8246},{"id":5,"name":6,"surname":7,"biography":8,"web":9,"slug":10},[8297,8298,8299,8300,8301,8302,8303],{"id":172,"name":5602,"slug":5603},{"id":164,"name":1033,"slug":1034},{"id":114,"name":407,"slug":408},{"id":123,"name":8253,"slug":8254},{"id":273,"name":1037,"slug":1038},{"id":287,"name":410,"slug":411},{"id":13,"name":413,"slug":414},{"duration":5584,"lections":984,"tests":5,"testsQuestions":273,"rating":5585,"packageCoursesMaxPrice":5079,"packageCoursesTotalPricesPerLicenceLength":8305,"packageCourses":5,"minPeriodForRating":5590},{"183":5079,"365":5587,"730":5588,"-1":5589},[],"2020-01-08T00:00:00.000Z",{"id":867,"name":8196,"slug":8197,"previewImage":8309,"description":8310,"description_mini":8198,"price":1995,"priceVariants":8311,"structure":8318,"type":392,"introductionVideo":8635,"packageCourses":8640,"coursePackages":8641,"relatedCourses":8646,"authors":8653,"categories":8655,"url":8199,"isFree":416,"counts":8660,"variant_title":48,"variant_description":48,"variants":8664,"status":50,"date_published":8665},{"id":8201,"width":1991,"height":1992},"Vyzkoušej si přijímačky nanečisto z matiky **v pohodlí domova**.\n\nČekají tě **dva reálné přijímací testy z matematiky** se vším všudy.\n\n- V kurzu uslyšíš přesné **pokyny**, které při skutečném přijímacím řízení bude zadavatel číst.\n- Oba testy jsou precizně zpracované podle všech standardů Cermatu.\n- Nebude chybět to nejdůležitější - testy si společně s Markem opravíš a vyhodnotíš.\n\n**Zjisti, jak na tom jsi a jak jsi připravený\u002Fá na přijímačky z matiky.**\n\nPřijímačkami nanečisto tě provede skvělý lektor Marek Valášek.\n\nCo tě čeká:\n------------\n\n1.  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