Vector Subspace | Basis & Dimension | Examples Of Basis | Linear Algebra

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This video lecture of Vector Subspace | Basis & Dimension | Examples Of Basis | Linear Algebra | Problems & Concepts by GP Sir will help Engineering and Basic Science students to understand the following topic of Mathematics:
1. What is Basis and Dimension Of Vector Space ?
2. Definition Of Basis and Dimension Of Vector Space.
3. Examples Based on Basis and Dimension Of Vector Space.
4. Short Trick To Find Basis and Dimension Of Vector Space.
5. This is part Of Linear Algebra
#LinearAlgebra #VectorSpace #BasisAndDimension #LinearlyIndependent #Linearlydependent #EngineeringMahemaics #BSCMaths #GATE #IITJAM #CSIRNET
This Concept is very important in Engineering & Basic Science Students. This video is very useful for B.Sc./B.Tech & M.Sc./M.Tech. students also preparing for NET, GATE and IIT-JAM Aspirants.
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Time Stamp
Basis and Dimension-
0:00 | An intro
0:15 | Topic introduction
1:08 | Basis
2:16 | Example
3:49 | Dimension
4:17 | Finite dimensional vector space
4:27 | Infinite dimensional vector space
4:46 | Examples
6:04 | Example 1 (Theorem statement)
8:11 | Example 2
8:59 | Example 3
11:06 | Example 4
13:34 | Example 5
14:24 | Conclusion of video
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Dr.Gajendra Purohit

Пікірлер: 366

  • @gajendrapurohit
    @gajendrapurohit4 жыл бұрын

    Thanks for your comment, your appreciation always motivate us to do such kind work. Join Telegram Channel : t.me/mathsbygpsir Instagram Handle : instagram.com/dr.gajendrapurohit/ Facebook Page : facebook.com/Dr-Gajendra-Purohit-453775988491992/ Unacademy : unacademy.com/@Dr-GajendraPurohit Link to B.Sc. Maths Playlist : bit.ly/34tTTdc Link to Engineering Maths Playlist : bit.ly/2OQ7Uvd Link to IIT-JAM Maths Playlist : bit.ly/2sh9pei Link to GATE (Engg.) Maths Playlist : bit.ly/35EAPct Link to IAS Optional Maths Playlist : bit.ly/2rwkOqj Link to CSIR NET Maths Playlist : bit.ly/2R8sUjV Link to Aptitude Playlist : bit.ly/3ewDR7z Link to Mathematical Physics Playlist : bit.ly/2NvRHLJ Link to Abstract Algebra Playlist : bit.ly/2A70LUb Link to General Aptitude For CSIR NET : bit.ly/2ZeWpma Follwing Topics are also Available 1. Differential Calculus : bit.ly/2OTYXB0 2. Integral Calculus : bit.ly/34rLA1R 3. Differential Equation : bit.ly/37IOlO1 4. Partial Differential Equation : bit.ly/2OM5iyA 5. Complex Analysis : bit.ly/2OP8hGp 6. Numerical Analysis : bit.ly/2QYVQuy 7. Integral Transform (Laplace, Fourier & Z-Transform) : bit.ly/37HRKg9 8. Statistics & Probability : bit.ly/2DmOt7Z 9. Operation Research : bit.ly/2pYYRjp 10. Matrices (Linear Algebra) : bit.ly/2OOBSzO 11. Fourier Series : bit.ly/34u7iC9 12. Vector Calculus : bit.ly/2qICwXO 13. Theory Of Equation : bit.ly/2XU9y33 14. Special Function & Series Solution : bit.ly/2XRSU4l 15. Infinite Series : bit.ly/37K6gUI 16. Group Theory : bit.ly/3ieUze2 Please share it with your Friends Thanks Dr.Gajendra Purohit

  • @reeselarry4207

    @reeselarry4207

    3 жыл бұрын

    Pro trick: watch series on InstaFlixxer. Me and my gf have been using it for watching loads of movies these days.

  • @justiceadriel8585

    @justiceadriel8585

    3 жыл бұрын

    @Reese Larry Yup, been using instaflixxer for since december myself =)

  • @nikolaisawyer2392

    @nikolaisawyer2392

    3 жыл бұрын

    @Reese Larry Yea, been using instaflixxer for since november myself :)

  • @sanjayguptamathematics431

    @sanjayguptamathematics431

    2 жыл бұрын

    Sir plz give your contact number

  • @ubaidrajput3703

    @ubaidrajput3703

    5 ай бұрын

    Ap smjha rhe ho, ya sirf English prh rhe ho,,, English prhna to hame v ata hai

  • @shubhamjain2789
    @shubhamjain27892 жыл бұрын

    Sir your teaching speed is so fast so it is difficult for new student to understand

  • @shamswazir7509

    @shamswazir7509

    Жыл бұрын

    You can slow speed in settings. Just click on setting icon and go to play back speed and where you set speed by your choice

  • @VivekSingh-pl4kz

    @VivekSingh-pl4kz

    Жыл бұрын

    Sahi hai

  • @shashinilaratna2922

    @shashinilaratna2922

    Жыл бұрын

    @@shamswazir7509fast in terms of syllabus

  • @jishantamboli9844

    @jishantamboli9844

    Жыл бұрын

    You are right teaching speed is too fast

  • @payalswaroop2004

    @payalswaroop2004

    10 ай бұрын

    Voice ki baat nahi hai jaldi jaldi bolte hain. Usnki kisi bhi topic ko padhane ki speed fast hai

  • @vaishnavisingh6595
    @vaishnavisingh6595 Жыл бұрын

    It was the best time when sir used to teach on the green board. Now everything is in fast forward motion and some of the things just blow up your mind

  • @The_RandomGuy

    @The_RandomGuy

    5 ай бұрын

    these chapters requires such treatment

  • @pmfacts9354

    @pmfacts9354

    5 ай бұрын

    I think these chapter is conceptual so it will take time

  • @SnehaSingh-ts7oi
    @SnehaSingh-ts7oi2 жыл бұрын

    Hi Sir. I have understood these topics from your video really well. But you haven't covered examples to find basis of a vector space. Please add that also.

  • @Wolverine_261

    @Wolverine_261

    Жыл бұрын

    Haa missing hai

  • @punamchatterjee1027
    @punamchatterjee10273 жыл бұрын

    Sir please give us a video about linear span and deletion theorem....and their examples

  • @utube5064
    @utube5064 Жыл бұрын

    Sir I can see mark difference in your style of teaching. When you started youtube channel with chalk and board in a classroom, that was amazing. Chalk and duster can never loose charm and these presentation can never match classroom boards. Sir can we go back to board where you solve problems with your own hand not show us these presentation.

  • @pranavshivhare

    @pranavshivhare

    Жыл бұрын

    +1

  • @belcofalcon4279

    @belcofalcon4279

    Жыл бұрын

    +1

  • @umaidmanzoor5659

    @umaidmanzoor5659

    Жыл бұрын

    +1

  • @adarshraj_7903

    @adarshraj_7903

    Жыл бұрын

    +1

  • @Someone_1758

    @Someone_1758

    8 ай бұрын

    +1

  • @uvchouhan4353
    @uvchouhan4353 Жыл бұрын

    ❤️❤️❤️❤️thank you very much sir ... Wonderful explanation

  • @fooditems9839
    @fooditems98393 жыл бұрын

    I'm really thankful for you sir ❤️❤️

  • @waqashashmi4061
    @waqashashmi40613 жыл бұрын

    Thank you so much Sir I have completed vector space topic completely Love and respect from 🇵🇰

  • @usama2073

    @usama2073

    2 жыл бұрын

    Hey can u help me in linear algebra problems?

  • @nadeemdanish1868
    @nadeemdanish18688 ай бұрын

    he is like giving presentation in first semester.

  • @MathsForkFeelTheConcept
    @MathsForkFeelTheConcept4 жыл бұрын

    Your video just amazing sir 👌It a very helpful sir thankuu so much🙏

  • @miklejitendrakumar5585
    @miklejitendrakumar55853 жыл бұрын

    You are great and osm u teach every topic very smoothly and verry esey way I verry like ur classes

  • @vidyasagarreddykarru1131
    @vidyasagarreddykarru11315 ай бұрын

    Thank you sir. Very Good Explanation.🙂

  • @nikitamaurya4518
    @nikitamaurya45189 ай бұрын

    gained a new subscribed! thank you for saving my time!

  • @manojkumardandapat2037
    @manojkumardandapat20373 жыл бұрын

    Thank u Sir.. God bless u

  • @pranitachadha5608
    @pranitachadha56082 жыл бұрын

    Thank you so much sir your videos are very helpful. Please make a video on span also.

  • @panchram3638
    @panchram36383 жыл бұрын

    Love u sir...always..❣❣❤❤

  • @ranjitharanjitha2231
    @ranjitharanjitha22313 жыл бұрын

    Excellent sir. Ur teaching is awesome..... I can understand ur teaching.... It is very useful for every student..... Thanks A lot sir

  • @mathswithoutfear2224
    @mathswithoutfear22244 жыл бұрын

    I m always waiting for ur videos

  • @preetisaini2935
    @preetisaini29352 жыл бұрын

    Mind blowing sir aapse pdhkr Humko bhot achha laga

  • @sankalpgupta2255
    @sankalpgupta2255 Жыл бұрын

    Sir you teach very well..❣️....you know how to explain the concept❣️ but please don't try to complete the video in one shot as you began to stammer after being exhaust!

  • @BRIGHTEDUCATION6900
    @BRIGHTEDUCATION69003 жыл бұрын

    You are the magician of mathematics sir

  • @vmgphysicsclasses1072
    @vmgphysicsclasses10722 жыл бұрын

    Sir aap k video se bahut jda help hoti hai . great sir

  • @akashchaturvedy2677
    @akashchaturvedy26774 жыл бұрын

    A lot of thanks for upload a video

  • @vinnysahni8661
    @vinnysahni86612 жыл бұрын

    Thank you Sir , for the great videos. I have one request sir , if you can tell which book you have used foe this particular video. The reason for the same is I m doing MA Maths from LPU and the textbook have same numericals . So is there any particular author's book that you would advise for Linear Algebra

  • @anshikachauhan9388
    @anshikachauhan93887 ай бұрын

    Thanks sir for this video ❤

  • @Dc78498
    @Dc784983 жыл бұрын

    Useful video ❤️

  • @AnilVerma-gv2mt
    @AnilVerma-gv2mt4 жыл бұрын

    It's very useful video lecture

  • @abhinandanjain2399
    @abhinandanjain2399 Жыл бұрын

    Thank you so much sir 🙏. 🙏

  • @susantapradhan228
    @susantapradhan2283 жыл бұрын

    Thank you sir❤️

  • @official-uttarakhand
    @official-uttarakhand4 ай бұрын

    Sir explained 🙏 So that S={ (1,2,4), ( 1,0,0), (0,1,0), (0,0,1) } is a linearly dependent subset of the vector space V3 (R) Where R is the field of real numbers.

  • @MathematicswithRohit

    @MathematicswithRohit

    2 ай бұрын

    Hello Students you can watch my Linear Algebra Playlist if you are not able to understand here. Please visit once and see and subscribe if you like the videos 😊

  • @tons143..7
    @tons143..73 жыл бұрын

    Thank you so much sit

  • @lalitbaruah7024
    @lalitbaruah70242 жыл бұрын

    Well explained 👍

  • @pavneetpreetkaur7801
    @pavneetpreetkaur7801 Жыл бұрын

    Very helpful video sir

  • @monukaushal530
    @monukaushal5309 ай бұрын

    Thanks you so much sir 😊 🙏

  • @mathematicsbyvivekanand2375
    @mathematicsbyvivekanand23753 жыл бұрын

    Really sir you are great

  • @apurbanandi9175
    @apurbanandi91754 ай бұрын

    Thank you Sir!

  • @navitakushwaha1549
    @navitakushwaha15495 ай бұрын

    Thank you sir

  • @nikhilprajapati959
    @nikhilprajapati9592 жыл бұрын

    Thank you sir for the video. Sir, please make a video on span. Please sir🙏🙏

  • @anshikagupta8017
    @anshikagupta80172 жыл бұрын

    Thank you so much sir

  • @solveit1
    @solveit13 жыл бұрын

    Tnx sir ,you are great

  • @omkar1070
    @omkar1070 Жыл бұрын

    Well explained sir ❤❤

  • @genius5376
    @genius53763 жыл бұрын

    Thank you sir from mauritius.

  • @poojasherawat615
    @poojasherawat6154 жыл бұрын

    Guru Purnima ki bahut bahut subhhkamnae Guru g............ Aapne hme free of cost CSIR net ka gift diya........................ Thanks so much 😍

  • @GurwinderMaurMaths
    @GurwinderMaurMaths4 жыл бұрын

    Very helpful

  • @lifeawesome2414
    @lifeawesome24143 жыл бұрын

    Sir apne hmara jeevan sudhaar diya 1st yr than 2nd thanku sir

  • @SahilKumar-zl6me
    @SahilKumar-zl6me2 жыл бұрын

    This video helped me in my viva

  • @onedayonemovie4022
    @onedayonemovie4022 Жыл бұрын

    those who where confused at 12:05 . a1ba is cut from both side . a2da is correct no need to cross it. taking a2da on l.H.S then only you will get ad-bc not equal to zero. Thankyou . Love from Nepal

  • @jicy5593
    @jicy55933 жыл бұрын

    Very good presentation sir. Actually I am a teacher, I want to know which platform are you using for this presentations. It is really great for understanding..

  • @amitoshkumar3276

    @amitoshkumar3276

    2 жыл бұрын

    Unacademy he is using

  • @dibyajyotigogoi2640
    @dibyajyotigogoi26402 жыл бұрын

    Sir ur are great

  • @satyasanatani6541
    @satyasanatani6541 Жыл бұрын

    Bsc compete.... All semester with GP sir... Thanks a lot sir❤❤❤🥰

  • @shailanshvishwakarma4869
    @shailanshvishwakarma48693 жыл бұрын

    Thank you 😊❤️💖😍

  • @Ranjana-123
    @Ranjana-1233 жыл бұрын

    Thanku sooo muchh sir

  • @Rp63888
    @Rp638882 жыл бұрын

    Nice class sir 🙏🙏🙏

  • @LRGClasses
    @LRGClasses3 жыл бұрын

    Happy teacher's day Sir

  • @LRGClasses

    @LRGClasses

    3 жыл бұрын

    Love you Sir

  • @luckyRchouhan5

    @luckyRchouhan5

    3 жыл бұрын

    @@LRGClasses okk

  • @karishmabaghel866
    @karishmabaghel8664 жыл бұрын

    Thank you so much sir🙏🙏🙏🤗 aapki video bhut hi jada helpful hoti hai... Aapka pdhne ka tarika bhut hi acha hota sab kuch bhut ache se clear hota hai😇🙏🙏

  • @himangnisahu606
    @himangnisahu6064 жыл бұрын

    Sir how to chose the dimensions please explain and give some questions related to that video sir and thank you sir....... This is very helpful.......

  • @shashidharrenumala7499

    @shashidharrenumala7499

    3 жыл бұрын

    Yes himangini

  • @beautifullworld95
    @beautifullworld952 жыл бұрын

    Sir plz tell me the result, why dimension of C(Q), R(Q) is infinite?

  • @risckstar9366

    @risckstar9366

    2 жыл бұрын

    Yes I don't ever know 😢😢

  • @risckstar9366

    @risckstar9366

    2 жыл бұрын

    I have many questions

  • @davidgamerz2116

    @davidgamerz2116

    Жыл бұрын

    Cause it's basis are infinite

  • @kamalbhatta9559
    @kamalbhatta9559 Жыл бұрын

    thank you sir❤❤

  • @lot-potjokes...3290
    @lot-potjokes...3290 Жыл бұрын

    Sir please give more explanation so that i can understand easily

  • @pabanbaishya5815
    @pabanbaishya58152 жыл бұрын

    Thank you ❤️❤️☺️❤️☺️ Sir

  • @heartbeat5237
    @heartbeat52372 жыл бұрын

    Love you sir 💓💓💗💕

  • @mathsloversjn3453
    @mathsloversjn34533 жыл бұрын

    Nice explain sir

  • @RajkumarGupta-gd9uo
    @RajkumarGupta-gd9uo Жыл бұрын

    I am watching this video playing 2X speed....And understand.... Thanks 🙏🙏🙏 sir

  • @journeywithkoushik1932
    @journeywithkoushik19324 жыл бұрын

    Thank you so so much sir for ur fantastic teaching process,I'm very grateful to you Sir🙏....but I need more class of linear algebra...

  • @abhinandankumar4272
    @abhinandankumar42724 жыл бұрын

    Thanks sir very nice sir

  • @malikishan000
    @malikishan0003 жыл бұрын

    Very nice sir

  • @amitjha1072
    @amitjha10723 жыл бұрын

    Mera to correspondence course sir k lecture ki wajah se chal rha h aur exam bhi achhe marks se clear ho rhe h.Thanks to you sir. But the clarity which i got in PI & CI is not coming here.

  • @hrushikeshvardhan3626
    @hrushikeshvardhan36266 ай бұрын

    thanks sir

  • @gunasundariguna6733
    @gunasundariguna67332 жыл бұрын

    Sir your teaching is well and good and one more request pls little bit english tell me

  • @divyanshibarman2324
    @divyanshibarman2324 Жыл бұрын

    Tomorrow is my maths exam I want dimensions theorems videos please

  • @shrutigupta250
    @shrutigupta2503 жыл бұрын

    Really useful for bcom students too. Great video

  • @2134ssss
    @2134ssss3 жыл бұрын

    best explanation sir...thanks a lot🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏

  • @geetikasain9874
    @geetikasain98743 жыл бұрын

    Thank u sir

  • @Rakeshkumar-jf4ty
    @Rakeshkumar-jf4ty Жыл бұрын

    Nice sir 🙏 🙏 🙏

  • @amaanali1009
    @amaanali10093 жыл бұрын

    sir please solve more examples because exams mei itna easy sawaal nhi aata and we don't know how to proceed with tough questions

  • @rupeshmishra-vnc
    @rupeshmishra-vnc4 жыл бұрын

    Lv uuu sir ur teaching skill is fine. I understand every topic

  • @AnjaliTiwari862
    @AnjaliTiwari8624 жыл бұрын

    Hydrodynamic and classical mechanics nd basic topology ke topics par video bnaeye please sir

  • @mp-ed4zl
    @mp-ed4zl Жыл бұрын

    Sir very good 😊😊😊👍👍👍

  • @geoplusmath869
    @geoplusmath8692 жыл бұрын

    Thanks sir g love from Pakistan

  • @AnilVerma-gv2mt
    @AnilVerma-gv2mt4 жыл бұрын

    Thanx sir jii

  • @MohammadMunaam
    @MohammadMunaam3 жыл бұрын

    This video helped me in my assignments 😃

  • @usama2073

    @usama2073

    2 жыл бұрын

    Hii

  • @MohammadMunaam

    @MohammadMunaam

    2 жыл бұрын

    @@usama2073 hello

  • @MohammadMunaam

    @MohammadMunaam

    2 жыл бұрын

    @@usama2073 nahi Bhaijaan main CS se btech kar raha hu 😅

  • @usama2073

    @usama2073

    2 жыл бұрын

    @@MohammadMunaam kaun sa semester chal raha?.. Aur aap kahan se ho?

  • @MohammadMunaam

    @MohammadMunaam

    2 жыл бұрын

    @@usama2073 apko kya karna janke vese 😅

  • @akashchaturvedy2677
    @akashchaturvedy26774 жыл бұрын

    Please sir provide us complete course in linear algebra

  • @ritikashahu2426
    @ritikashahu24262 жыл бұрын

    Sir pls upload video on linear span🙏🏻🙏🏻

  • @tpsicmin
    @tpsicmin2 жыл бұрын

    Nice

  • @rashmigupta1680
    @rashmigupta16804 жыл бұрын

    Sir isse related questions ki video B upload kro.... Plz

  • @gursimranjeetsingh9831
    @gursimranjeetsingh98313 жыл бұрын

    Sir plz upload a video on linear span

  • @arkaprabhasaha8203
    @arkaprabhasaha8203 Жыл бұрын

    Sir there is no where mention that suppose vector (1,0,0), (0,1,0), (1,1,1) should span R3 in order to be Basis. Is that not required in college level?

  • @parnikaagarwal259
    @parnikaagarwal2593 жыл бұрын

    Sir, aapne essa phale video m bataya tha..linear combination m likhne k liya relation hona chyiya ..aur relation toh linear depend m hota hai toh LI ko Linear combination m ku likh rah hai aap?

  • @Rakshit_Jain

    @Rakshit_Jain

    2 жыл бұрын

    Li ko bhi linear combination m likh skte h But wha par sirf ek solution hoga. Scalars=0

  • @Nisarahmad-vh7jb
    @Nisarahmad-vh7jb8 ай бұрын

    Sir G please make a video on "change of bases" in linear algebra

  • @knowledgefounder896
    @knowledgefounder8964 жыл бұрын

    sir please start the Topology lecture

  • @M-kamran-awan
    @M-kamran-awan Жыл бұрын

    Aslamolikum sír request to discuss the Galvois theory kindly

  • @bhupenderchauhan7435
    @bhupenderchauhan74354 жыл бұрын

    Dear sir please provide link for linear transformation

  • @kabeerbutt62
    @kabeerbutt623 жыл бұрын

    Shehzaday Sir....... Love from pakistan...

  • @ashishbisht6841
    @ashishbisht68412 жыл бұрын

    Sir In example 3 , c=1/6 is wrong actually its c= 1/9. Just for correction sir .... Your vedios are very helpful for us sir . Thank you sir

  • @adksongs1524

    @adksongs1524

    Жыл бұрын

    Bro how did u get that also , I don't know why I didn't get any of these values

  • @sonit9707

    @sonit9707

    Жыл бұрын

    It can only mean one thing.

  • @ashishbisht6841

    @ashishbisht6841

    Жыл бұрын

    What sonit?

  • @vaishnavisingh6595

    @vaishnavisingh6595

    Жыл бұрын

    @@adksongs1524 yes even I didn't get it

  • @nitinnayal2540
    @nitinnayal25402 жыл бұрын

    sir lease make video on dual sace also and invertiblity of linear transform

  • @AnjaliTiwari862
    @AnjaliTiwari8624 жыл бұрын

    Sir aap abstract algebra msc ke sabhi topic par video bnaeye please sir I request you please sir

  • @siddhichaudhary8007
    @siddhichaudhary80074 жыл бұрын

    sir aapne upload kiya kya dimension wale mcqs

  • @kms8320
    @kms83203 жыл бұрын

    bahot mast kam karte ho aap.

  • @usama2073

    @usama2073

    2 жыл бұрын

    Hii

  • @siddhichaudhary8007
    @siddhichaudhary80074 жыл бұрын

    iske uper based mcqs short tricks wale video banao sir plxzzz