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Vector Subspace | Subspace Theorems & Examples | Linear Algebra

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This video lecture of Vector Subspace | Subspace Theorems & Examples | Linear Algebra | Problems & Concepts by GP Sir will help Engineering and Basic Science students to understand following topic of Mathematics:
1. What is vector Subspace ?
2. Definition Of Vector Space Subspace
3. Proof Of Necessary and Sufficient Condition For Subspace.
4. Proof Of various Theorems and Examples Of Vector Subspace
5. This is part Of Linear Algebra
#LinearAlgebra #VectorSpace #Subspace #Theorems
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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 NET, GATE and IIT-JAM Aspirants.
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Time Stamp
Vector subspace -
0:00 | An intro
0:17 | Topic introduction
1:22 | Vector subspaces
2:37 | Theorem 1
8:34 | Theorem 2
13:01 | Problem 1
15:28 | Problem 2
17:33 | Problem 3
20:09 | Conclusion of video
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Dr.Gajendra Purohit

Пікірлер: 214

  • @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

  • @haseebyaseen1401

    @haseebyaseen1401

    3 жыл бұрын

    @Emiliano Alex is it paid?

  • @MathwithSahill

    @MathwithSahill

    2 жыл бұрын

    Sir please send the PDF of the book

  • @aniketbhise8208
    @aniketbhise82083 жыл бұрын

    Sir I tell you one thing, the way of your teaching is excellent and another one thing is that sir you tech on blackboard or greenboard by writing that way is very effective. Again thank you very much Sir 👍🥳🥰

  • @mathsbyluvkesh1173
    @mathsbyluvkesh11734 жыл бұрын

    Thank you so much sir for starting vector space. Sir meine vector space other channel pe bhi padha h but jis easy method se aap padhate ho or koi nhi padhata

  • @ayushlohia2992
    @ayushlohia29923 жыл бұрын

    Thankyou sir.... vector subspace samajne m badi dikkat hui but apki video ne bahut help kari... Thanks a lot sir.

  • @biswajitbarik1077
    @biswajitbarik10774 жыл бұрын

    Bahut bahut sukriya sir....🙏

  • @knalins
    @knalins Жыл бұрын

    Thanks Sir, Your Video help me to do well in my academics

  • @priyaparjapti5480
    @priyaparjapti54803 жыл бұрын

    Very helpfull video thank u sir🙏

  • @49seemayadav65
    @49seemayadav654 жыл бұрын

    Thanku so much sir. Aapka pdaya hua bhut jaldi smaj me aa jata h again thanks a lot sir.

  • @divyanshuranjan2368
    @divyanshuranjan23684 жыл бұрын

    Sir your videos help me a lot... regarding my gate examination... thanks sir

  • @Xyzzz8088
    @Xyzzz80883 жыл бұрын

    Thanks Sir ,Your Explanations are really great👌🏻👌🏻👌🏻👌🏻👌🏻

  • @Ayodhyawale933
    @Ayodhyawale9333 жыл бұрын

    Sir you videos is very helpful to everyone

  • @aniketbhise8208
    @aniketbhise82083 жыл бұрын

    Thank you very much Sir 👍👍

  • @karishmabaghel866
    @karishmabaghel8664 жыл бұрын

    This video is really helpful for my bsc exam...thank you sir🙏🙏✨

  • @MathswithKM

    @MathswithKM

    4 жыл бұрын

    Visit my channel for ring theory videos.

  • @karishmabaghel866
    @karishmabaghel8664 жыл бұрын

    Thank you so much sirr 🙏🙏🙏

  • @zafarabbas8287
    @zafarabbas82872 жыл бұрын

    Nice sir .I have gain a lot from your lecturs.Zafar abbas from pakistan.thanks a lot

  • @aimalkhankakar8030
    @aimalkhankakar80302 жыл бұрын

    Thanks sir grt effort

  • @artistankitmadulya4568
    @artistankitmadulya45683 жыл бұрын

    Thank you guru, ji

  • @ManlyMadhu123
    @ManlyMadhu123 Жыл бұрын

    I am from IITHyderabad sir your lectures are so nice and helpful for me sir

  • @Unlhd_tr
    @Unlhd_tr Жыл бұрын

    Sir I am studying BSC Maths in the UK and I love your videos so much! They’re so helpful Thank you

  • @aadityakumar903

    @aadityakumar903

    Жыл бұрын

    Uk..? Uttrakhand..!??

  • @satyamjha4758

    @satyamjha4758

    Жыл бұрын

    United Kingdom Britain😅

  • @DELTA_official

    @DELTA_official

    Жыл бұрын

    @@aadityakumar903 ise type ky question exam my bi atty hai 🤣

  • @mahendrajas540

    @mahendrajas540

    6 ай бұрын

    Bcs from England 😮😮😮😮

  • @janababd5617
    @janababd56173 жыл бұрын

    Thank you sir ❤️❤️❤️

  • @vikashsholankiofficial4281
    @vikashsholankiofficial42813 жыл бұрын

    Thank you very much sirji

  • @krishanubakshi7060
    @krishanubakshi70603 жыл бұрын

    thank you so much sir

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

    Thanks sir for vide0

  • @youtubemaths
    @youtubemaths3 жыл бұрын

    Thanks 🙏

  • @nasrinakter5873
    @nasrinakter58732 жыл бұрын

    Thanks a lot sir☺️

  • @sumanyadav4921
    @sumanyadav49213 жыл бұрын

    Thanks for more videos upload

  • @manojkumardandapat2037
    @manojkumardandapat20373 жыл бұрын

    Excellent Sir

  • @brajashekhar6820
    @brajashekhar68203 жыл бұрын

    Thank u so much sir ur teaching style is awesome

  • @ankitajoshi666
    @ankitajoshi6663 жыл бұрын

    Amezing sir😊😊

  • @pranav3813
    @pranav3813 Жыл бұрын

    Thx for video

  • @themathmotivor.
    @themathmotivor.3 жыл бұрын

    Sir you are great

  • @abhishekprajapat5305
    @abhishekprajapat53053 жыл бұрын

    Thanks sir 🙏😊

  • @satendrakashiyam771
    @satendrakashiyam7714 жыл бұрын

    Thabks so much sirji

  • @itsmeeee3288
    @itsmeeee328810 ай бұрын

    Really sirrr.. apko bohot saraaaa thank you bolne ki jarurat hai😅🎉😊❤you are great sir💯✅🙆🏻‍♀️

  • @Rakeshkumar-jf4ty
    @Rakeshkumar-jf4ty Жыл бұрын

    Very nice sir 🙏 🙏 🙏

  • @bikashdutta2585
    @bikashdutta25852 жыл бұрын

    Thanks sir

  • @anjalibalihar7227
    @anjalibalihar72272 жыл бұрын

    Thank you sir ☺️☺️☺️

  • @sumitkashyap5469
    @sumitkashyap54693 жыл бұрын

    Thanks you sir 🙏🙏🙏🙏

  • @adminjoey1654
    @adminjoey1654 Жыл бұрын

    Can't Imagine My Degree Without Him ❤️

  • @ManlyMadhu123

    @ManlyMadhu123

    Жыл бұрын

    then tyr to don't imagine

  • @priyanshubehera8085

    @priyanshubehera8085

    Жыл бұрын

    @@ManlyMadhu123 🤣🤣

  • @AnimewithPraveen

    @AnimewithPraveen

    6 ай бұрын

    😂😂😂😂😂

  • @atindramaurya5869
    @atindramaurya58693 жыл бұрын

    Wow 🥰 Amazing ❤️ Sr aapka padhane ka tareeka lajwab hai ❤️ mind blowing guru ji 🔥

  • @Monika_singh2699
    @Monika_singh26994 жыл бұрын

    Thanks so muchh sir ji🙏🙏.... Sir, your teaching style/ method is amazing..... You are best and great educator.....

  • @biswajitbarik1077

    @biswajitbarik1077

    4 жыл бұрын

    Aapne sahi kaha Monica ji...maine jindagi mein eisa teacher kabhi Nahin dekha... subject chahe jitna v kathin kyun na ho jab gajendra sir padhate hein na yaar sab kuch samajh mein aa jata hai... hat's up sir...

  • @garrysingh385

    @garrysingh385

    4 жыл бұрын

    Sir g tusi differential equation me btaya tha ordinary point me bare me . sir g ordinary poins infinite ho sekde ne according to that

  • @kavyam.v8089
    @kavyam.v80893 жыл бұрын

    THANKS 🙏🏽SIR

  • @MWASI-kk8nn
    @MWASI-kk8nn Жыл бұрын

    बहुत-बहुत शुक्रिया

  • @ManlyMadhu123
    @ManlyMadhu123 Жыл бұрын

    sir in second problem how do you now it's a inear equation and actually it's a 2nd order equation not a 2nd degree equation

  • @PhysicsNomad01
    @PhysicsNomad01 Жыл бұрын

    Sir, in 5:23 we already have W is closed under vector addition and scalar multiplication. Then why do we need to prove them again by taking alpha=beta = 1 for W is closed under addition and beta=0 for W is closed under scalar multiplication ?

  • @mixing591
    @mixing5914 жыл бұрын

    Sir inner product space chapter 10th by jeevan sans publications upload kr do please request 4th section pura ho jaye ga

  • @gareenamasti3799
    @gareenamasti37992 жыл бұрын

    Sir, your teaching style is so pretty I fall in love of mathematics 😘😘😘

  • @salonikumari4208
    @salonikumari42084 жыл бұрын

    What is the difference between what you teach here in KZread and in unacademy plus

  • @himanshukhandelwal1982

    @himanshukhandelwal1982

    3 жыл бұрын

    Live Classes ,PYQs and also other teachers are on unacademy Plus

  • @AkankshaSunaar-ro1zd

    @AkankshaSunaar-ro1zd

    Жыл бұрын

    Achcha to pdhaaa rhe

  • @viveksingh1m673
    @viveksingh1m6734 жыл бұрын

    Sir DU me MCA entrance me bsc math aata hai kya Aapka video helpful Hoga us exam me Aur kya aapne Pura math syllabus cover Kiya hai

  • @tpsicmin
    @tpsicmin2 жыл бұрын

    Nice

  • @htp2319
    @htp23193 жыл бұрын

    thanks

  • @Aman_Bhai_sidhu
    @Aman_Bhai_sidhu2 жыл бұрын

    Sir please ap range and null space par video bna dijae muja apka channel sa alag khi smj nhi ata sir you are unique teacher in India really

  • @sakthipriya9696
    @sakthipriya96964 жыл бұрын

    Thank you so much Sir. But it would be better if u add captions to all linear algebra videos sir😊

  • @prashantmishra5914
    @prashantmishra59143 жыл бұрын

    Sir... Is this series of linear algebra helps in the preparation of csir net? Plzz suggest sir 🙏🙏

  • @saaimatabassum4085
    @saaimatabassum40853 жыл бұрын

    Sir please solve more problems.

  • @FF....lover....
    @FF....lover....10 ай бұрын

    Hello sir I'm studying in USA your KZread classes are so helpful,great thanks.....for your classes🔥🔥🔥🔥

  • @soumenpati4133
    @soumenpati41334 жыл бұрын

    Sir thank you so much for your great explanation 🙏...sir pure mathematics ke part series and sequence ka topic par bohot jada video te humlogoki bohot help hoti sir,main is liye bata raha hu jo hum apka har lecture dekhta hu

  • @sreenjaysen927

    @sreenjaysen927

    4 жыл бұрын

    For linear algebra you should watch Dr. Strang's videos in MIT Opencourseware. Stop watching this crap.

  • @shahidnoorani8193
    @shahidnoorani81933 жыл бұрын

    sir aap college nahi jaane wale bando ke liye ek angel hai or meri dua hai aap hamesha healthy rahe. :)

  • @fooditems9839
    @fooditems98393 жыл бұрын

    Tooooooooooooo good sir

  • @shivanigusain5699
    @shivanigusain56993 жыл бұрын

    Sir plz make vedio in coinc section n polor from plz sir as soon as possible

  • @AbhishekSingh-xi4mw
    @AbhishekSingh-xi4mw2 жыл бұрын

    Sir you have provided such a great opportunity to crack the competitive exams ❤❤❤

  • @anilyadavgzp04
    @anilyadavgzp044 жыл бұрын

    Sir mechanics pe bhi video daliye

  • @manishabai1976
    @manishabai19764 жыл бұрын

    Sir ,RPSC 1st grade math ka syllabus our csir net ka syllabus ek hi h kya

  • @mdbadruddin9852
    @mdbadruddin98523 жыл бұрын

    Define vector space and subspaces mai ek video banaye please

  • @saurabhghule9982
    @saurabhghule99824 жыл бұрын

    Well done💯👍👏 sir I am your fan also

  • @garrysingh385
    @garrysingh3854 жыл бұрын

    Guys like the video.sir g bahut hard work kr re han

  • @kamaldeep8639
    @kamaldeep86394 жыл бұрын

    Sir Euclidean ring par video bnayiye please

  • @Namita_chawla
    @Namita_chawla4 жыл бұрын

    Sir...ring theory wala aage wala content bhi provide kro please please please

  • @inocentharsh439
    @inocentharsh4392 жыл бұрын

    Good explanation But speed is fast

  • @namonarayanmeena2000
    @namonarayanmeena20002 жыл бұрын

    Sir please upload the pdf notes also it will be helpful Please sir 🙏🙏🙏🙏

  • @mathematicsworld97
    @mathematicsworld974 жыл бұрын

    Sir can you plz tell me the solution of equation logx^2= 2logx in detail.

  • @mathematicsworld97

    @mathematicsworld97

    4 жыл бұрын

    @@urdeep01 I know it's a property of logarithmic function but I had a question in paper to find the solution of this equation .

  • @mathematicsworld97

    @mathematicsworld97

    4 жыл бұрын

    @@urdeep01 thanks

  • @Namita_chawla
    @Namita_chawla4 жыл бұрын

    Ideals wala topic pura nahi hai sir ring theory ka...please vo pura krwaeee please sir

  • @RinkiSingh-ij9zh
    @RinkiSingh-ij9zh2 жыл бұрын

    Hlo sir aap pahale khud se likhte the to achhe se samajh aata tha ab aap pahale se hi likhe ho aur bata rhe ho to utna nhi samajh aa rha

  • @atharva9076
    @atharva90762 жыл бұрын

    Thanks sir. i wish i could pay you instead of my college tuition :-(

  • @manishatomar4255
    @manishatomar42553 жыл бұрын

    Sir exam m dono theorem prove krni h kya

  • @familymagic-ig2ve
    @familymagic-ig2ve Жыл бұрын

    Namste guru ji

  • @anudhimishram6192
    @anudhimishram6192 Жыл бұрын

    Sir I want to suggest you something if you plz can teach little slower than it would be much helpful..otherwise you teach very well👌

  • @Ayesha_01257
    @Ayesha_01257 Жыл бұрын

    Good Good Good👍💓💓

  • @MuhammadZahid-wd6jv
    @MuhammadZahid-wd6jv3 жыл бұрын

    Kmall sir ji Bra acha samjaty hai ap👌👍

  • @srinityapadma5125
    @srinityapadma51253 жыл бұрын

    Thank you so much Sir... I got it here so much easy and simple than I thought it would be.../\

  • @ambikapatil6699

    @ambikapatil6699

    3 жыл бұрын

    Sir upsc mathematics ko bhi a videos dekh sakthe na sir

  • @learningwith---ashutoshyad9829
    @learningwith---ashutoshyad98293 жыл бұрын

    Best teacher for engineering or competitive mathematics

  • @letscrackupsc688
    @letscrackupsc688 Жыл бұрын

    Sir ye videos upsc k liye sufficient h

  • @Happy01976
    @Happy019764 жыл бұрын

    Di you know about exademy yiutibe cahnnel

  • @nimrahameed240
    @nimrahameed2403 жыл бұрын

    Sir! please can you give us an example as assignment, which is not a subspace of a vector space.

  • @sumanyadav4921
    @sumanyadav49213 жыл бұрын

    Sir please thoda slow padhaya kariye but you are best teach.

  • @kshamashreek6126
    @kshamashreek61263 жыл бұрын

    Okay... Is this BSc 6th Sem subject?

  • @mandeepsharma1981
    @mandeepsharma19819 ай бұрын

    ❤❤

  • @naeemahmed4738
    @naeemahmed47384 жыл бұрын

    Sir pdf mil sakta ha ap k notes ka?

  • @straightforward2027
    @straightforward20274 жыл бұрын

    Sir please launch math optional course of upsc in unacademy plus plzz sir

  • @AnilKumar-yy6bq
    @AnilKumar-yy6bq3 жыл бұрын

    Sir thoda slow pdaya kro plz

  • @vikaskr2606
    @vikaskr26062 жыл бұрын

    Sir please B. Sc 2yer mechanics ka video

  • @abhishekpokhrel9658
    @abhishekpokhrel96583 жыл бұрын

    I need a solution for : V=R^3. Show W = {(x,y,z) : 2x+y+2z=0} is subspace of V.

  • @akashsinghyadav1236

    @akashsinghyadav1236

    3 жыл бұрын

    It's a similar kind of problem , see if it helps Example 1: 𝑊={(𝑥,𝑦,𝑧):3𝑥−2𝑦+𝑧=0, 𝑥,𝑦,𝑧∈ℝ} is a subspace of ℝ^3. Let 𝛼=(𝑥_1,𝑦_1,𝑧_1 ) and 𝛽=(𝑥_2,𝑦_2,𝑧_2 ) be any two vectors in 𝑊 and 𝑐 be any scalar in ℝ. Then, 𝑐𝛼+𝛽=(𝑐𝑥_1+𝑥_2,𝑐𝑦_1+𝑦_2,𝑐𝑧_1+𝑧_2) and 3(𝑐𝑥_1+𝑥_2 )−2(𝑐𝑦_1+𝑦_2 )+𝑐𝑧_1+𝑧_2=𝑐(3𝑥_1−2𝑦_1+𝑧_1 )+3𝑥_2−2𝑦_2+𝑧_2=0. Therefore, 𝑐𝛼+𝛽∈𝑊 and 𝑊 is a subspace of ℝ^3.

  • @menekamahto6837
    @menekamahto68373 жыл бұрын

    👍👍👍

  • @tapaswinisahoo9520
    @tapaswinisahoo95204 жыл бұрын

    Pura vector space kab tab cover hoga

  • @Sidiiidiwdoewbwicisiwiw
    @Sidiiidiwdoewbwicisiwiw Жыл бұрын

    I am from IIT Bomabay CSE ,your videos are very helpfull

  • @tusharkukreja671

    @tusharkukreja671

    Жыл бұрын

    Hi I am from IIT Bidholi, Uttarakhand

  • @Siuuu18vk

    @Siuuu18vk

    6 ай бұрын

    Hi I am from IIT Dholakpur

  • @mathsaddicts1064
    @mathsaddicts10644 жыл бұрын

    Sir please suggest me one book that is helpful for more question for IIT jam paper after solving this book look like comfortable in jam paper question

  • @sachin.tiwarisachintiwari6838
    @sachin.tiwarisachintiwari68383 жыл бұрын

    Radhey Radhey sir

  • @SBKC.INDIRAPURAM
    @SBKC.INDIRAPURAM3 жыл бұрын

    Tension lene ki jrurat nhi hai ☺️☺️☺️

  • @themathmotivor.
    @themathmotivor.3 жыл бұрын

    Sir I am from Pakistan Allah bless you

  • @vikaskr2606
    @vikaskr26062 жыл бұрын

    Sir kon See book sey parhathy hay