Vector Subspace | Linearly Independent | Linearly Dependents Vectors | Linear Algebra

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This video lecture of Vector Subspace | Linearly Independent | Linearly Independent and Dependents Vectors | Linear Algebra | Problems & Concepts by GP Sir will help Engineering and Basic Science students to understand the following topic of Mathematics:
1. What are Linearly Independent and Linearly Dependent Vectors ?
2. Definition Of Linearly Independent and Linearly Dependent Vectors.
3. Examples Based on Independent and Linearly Dependent Vectors.
4. Short Trick To Find Linearly Independent and Linearly Dependent Vectors.
5. This is part Of Linear Algebra #LinearAlgebra #VectorSpace #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
Linearly independent and dependent vector-
0:00 | An intro
0:13 | Topic introduction
1:15 | Linearly dependent
2:09 | Linearly independent
3:25 | Problem 1
7:41 | Problem 2
9:18 | Problem 3
11:06 | Problem 4
12:11 | Relation between linearly dependent vectors
16:37 | Conclusion of video
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Dr.Gajendra Purohit

Пікірлер: 415

  • @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

  • @bhumikasharma2248

    @bhumikasharma2248

    3 жыл бұрын

    Sir please thoda slow padhya karo , it would be suitable for all students........

  • @syedakisa4949

    @syedakisa4949

    3 жыл бұрын

    Sir kindly exponential function ka b bata dain agr koi vector ki value exponential function ma a rahe ho to uss ko kaisy check krain gy linearly independent hy ya dependent

  • @satyendra3d

    @satyendra3d

    3 жыл бұрын

    Thanku sir for this session 🙏

  • @Dr.Haleem08

    @Dr.Haleem08

    3 жыл бұрын

    A set of n vectors 𝑣1,𝑣2,𝑣3,...,𝑣𝑛 v 1 , v 2 , v 3 , . . . , v n is linearly independent, if no vector in the set can be expressed as a linear combination of the remaining n+1 vectors. State whether the above statement is true or false.

  • @stayupdate_

    @stayupdate_

    3 жыл бұрын

    5R3+2R2 operation hoga 7:03 pe check kare aapne minus kiya hai

  • @sachinyadav4439
    @sachinyadav44396 ай бұрын

    Who is here just 1 day before exam 😅😂

  • @heembhavsar8622

    @heembhavsar8622

    4 ай бұрын

    Tum pass hua? 😁

  • @Studygear.09

    @Studygear.09

    4 ай бұрын

    I am on the date of exam

  • @user-nn8ft1ge8q

    @user-nn8ft1ge8q

    4 ай бұрын

    I also😂😂❤❤

  • @WonderQuestforKids

    @WonderQuestforKids

    4 ай бұрын

    Me 3 days before

  • @rajesh_aditya

    @rajesh_aditya

    4 ай бұрын

    Me 6 months , before☠️

  • @apugoswami140
    @apugoswami1403 жыл бұрын

    This Man helps us more than teachers of our institutions. Thanks A Lot Sir.

  • @ManishSharma-oe9in

    @ManishSharma-oe9in

    3 жыл бұрын

    ipu se ho kya?

  • @harmangoria7915

    @harmangoria7915

    2 жыл бұрын

    Sahi bilkul👍👍🤓

  • @Future118

    @Future118

    2 жыл бұрын

    Yes you are right

  • @gaitondebhau3378

    @gaitondebhau3378

    2 жыл бұрын

    Amazing hai gajendra purohit sir

  • @Amy-be6xp

    @Amy-be6xp

    2 жыл бұрын

    So true

  • @bytesfashion
    @bytesfashion Жыл бұрын

    Seeing your lecture day before my mid sem. You lectures are boon to the students.

  • @arsalanamin5206
    @arsalanamin5206 Жыл бұрын

    @Dr.Gajendra Purohit, I really appreciate your videos, as they are very awesome & helpful in true learning of the concepts. Below mentioned is a mistake in this video, for your reference. 1) At 6:50, the new equation will be (R3' = 5R3 + 2R2) and not (R3' = 5R3 - 2R2) as you mentioned, because there already exists, negative signs with the enteries of R2 Regards.

  • @janjyotiojah2421

    @janjyotiojah2421

    8 ай бұрын

    yes i had the same doubt. thanks for pointing it out

  • @nihalsahay5429
    @nihalsahay54292 жыл бұрын

    Because of your guidance we are passing our semester exams Thanks a lot.

  • @deepakyadav-nl6yy
    @deepakyadav-nl6yy2 жыл бұрын

    Thank Q Sir....U r extremely valuable to entire student fraternity

  • @AnkurKumar-cv9tp
    @AnkurKumar-cv9tp3 жыл бұрын

    Sir aap ko duniya ki sari khusi mile aur aap ki wajah se hi math ki Meri topic cover ho rahi

  • @vasusharma4327
    @vasusharma43272 жыл бұрын

    HOW CAN SOMEBODY BE SO GOOD AT SOMETHIN' hats off to u sir ..... really helpful that was ....! thanks a lot

  • @sahilrazakhan8312
    @sahilrazakhan83122 жыл бұрын

    Thanku so much sir .......there is no one who had cover this much of topics 💓....more power to you sir 💓

  • @saliqueahmad4277
    @saliqueahmad4277 Жыл бұрын

    Watching this video just before the exam...got some confidence. Thank you Sir.

  • @manojkumardandapat2244
    @manojkumardandapat22443 жыл бұрын

    Really Sir all the videos of u r very very useful us....U r such an excellent teacher .......Your all video ko dekhne se pehle like chaihai

  • @creatingmathematicians1004
    @creatingmathematicians10043 жыл бұрын

    Your video is very helpful in my GIC and PGT maths exam. Thankyuu

  • @shivamathsmagma4005
    @shivamathsmagma40052 жыл бұрын

    Your video is very useful for my university exam. thank you very much guru ji.

  • @anurashkaushik884
    @anurashkaushik8842 жыл бұрын

    Thanks you for making such videos to solve our problems in maths

  • @theinfinity3954
    @theinfinity39548 ай бұрын

    Mera math itna easy lagti hain।jabse aapko follow kiya tab se sir।

  • @deekshadhiman150
    @deekshadhiman15011 ай бұрын

    amazing content with crystal clarity .. thank you so much Sir..!

  • @jannatferdos2515
    @jannatferdos25157 ай бұрын

    this teacher help us more tham my institutions..thanks sir

  • @AjaySingh-ng4is
    @AjaySingh-ng4is3 жыл бұрын

    Nicely explained the concept, very much useful.

  • @codingismylife8959
    @codingismylife89593 жыл бұрын

    You are really good than all teachers thank you so much sir

  • @shobhnakumari2136
    @shobhnakumari21363 жыл бұрын

    Thank you sir for all the hardwork you do for us.

  • @_anuj_gupta
    @_anuj_gupta2 жыл бұрын

    Excellent examples and their explanations Amazing sir

  • @amrithajyothi8048
    @amrithajyothi80482 жыл бұрын

    You are amazing Sir ….simple and easy 💯

  • @jaymekaundun7665
    @jaymekaundun76652 жыл бұрын

    The dependency analogy at last is godly.

  • @diwatesanketsantosh5296
    @diwatesanketsantosh52963 жыл бұрын

    thanks sir , it is very helpful to revise

  • @sanadclasses6156
    @sanadclasses61564 жыл бұрын

    Thanks for sending this topic Victor

  • @Ati1254
    @Ati12543 жыл бұрын

    Thanks a lot🥰 Your video explanation is REALLY NICE.

  • @believeinyourself1165
    @believeinyourself11653 жыл бұрын

    Thank you sir ...you are so good in everything

  • @deeplaxmisingh1242
    @deeplaxmisingh12422 жыл бұрын

    Very helpful to clear the concept thank you so much Sir

  • @bindusharma7714
    @bindusharma77142 жыл бұрын

    Sir online me to kush bi smj ni ata hai but jbb se app ki class me pd rha hu but ache se smj ata hai sir you are too good thank you so mush 🙏

  • @jenaamarnath
    @jenaamarnath2 жыл бұрын

    End me sir ne bahut badiya example diya independent and dependent ka.

  • @irreplaceabletika28
    @irreplaceabletika283 жыл бұрын

    Thank you from nepal💕❣

  • @Animated_Stories111
    @Animated_Stories1112 жыл бұрын

    Thank you very muchh sir🙏❤️it helps a lot .......

  • @KumarBikashThoughts
    @KumarBikashThoughts3 жыл бұрын

    Thank you very much sir Your videos are most valuable sir

  • @njtrisha.njt10
    @njtrisha.njt103 жыл бұрын

    Thank you very much for this video ❤️

  • @sonikayadav5888
    @sonikayadav58882 жыл бұрын

    Really helpful sir

  • @SHRINIKETH-xd4nn
    @SHRINIKETH-xd4nn2 ай бұрын

    Thankyou sir 🙏 🙏🙏🙏with utmost sincere obeisance.

  • @Studentstudent94
    @Studentstudent942 жыл бұрын

    Thanku so much sir

  • @ayushburathoki6692
    @ayushburathoki66923 жыл бұрын

    THANKYOU HELPED A LOT

  • @WasimShaikh-jo4ry
    @WasimShaikh-jo4ry3 жыл бұрын

    Thank you so much sir for your valuable contents. Can you please provide the lecture slides? It would be highly appreciable sir.

  • @tapandey9735
    @tapandey97352 жыл бұрын

    Thank u 🙏🙏 so much sir your videos are too much helpful

  • @amessit10
    @amessit103 жыл бұрын

    just wow...fab explanation

  • @createownway.4238
    @createownway.42382 жыл бұрын

    Tq soo much sir this vdo was useful to me. 🙏.

  • @shivamanhar
    @shivamanhar3 жыл бұрын

    Thank you sir. When i read the book related to this topic then I have not understand any more. and I request to you sir please explain Norms.

  • @indianforces7052
    @indianforces70522 жыл бұрын

    Thank u very helpful 👍

  • @missmeenu4233
    @missmeenu42334 жыл бұрын

    Nice video sir...... Thank you sir!

  • @aneeshmamidi5614
    @aneeshmamidi5614 Жыл бұрын

    at timing 7.40, you said the vectors are linearly dependent as the rank is lesser than no.of equations but after solving the matrix, the values of the scalar are all equal to 0, then isn't that linearly independent?

  • @vaibhavmore37

    @vaibhavmore37

    Жыл бұрын

    same question !!!

  • @AngelChahal-of6xp
    @AngelChahal-of6xp3 ай бұрын

    Nice one video sir, concepts are fully cleared ❤❤ thanks for these types of videos sir ❤❤❤

  • @komalsaini017
    @komalsaini0172 жыл бұрын

    Thank yu so much sir....

  • @sakshu6549
    @sakshu65493 жыл бұрын

    Thank you for your this video 🤗

  • @nusratjan6353
    @nusratjan63532 жыл бұрын

    Thanks a lot sir ur the best

  • @criclovers7230
    @criclovers72302 жыл бұрын

    sir your teaching method is too much fantastic

  • @sanatan337
    @sanatan3373 жыл бұрын

    Thank you so much sir.

  • @Mrhacker78456
    @Mrhacker784565 ай бұрын

    Thank you so much sir❤

  • @mojeshkatta7937
    @mojeshkatta7937 Жыл бұрын

    Thank you sir for your great help

  • @radhe_radhe_1611
    @radhe_radhe_16112 жыл бұрын

    Thank you so much sir

  • @triteshkumar6918
    @triteshkumar69184 жыл бұрын

    Thanku sir u are inspiration for me

  • @makematheasy5679
    @makematheasy56793 жыл бұрын

    Your all vedios are so helpfull especially when you teach on this board. Kindly always use this board in your lectures...

  • @premkumarmandal2998
    @premkumarmandal29983 жыл бұрын

    Very helpful sir

  • @nationalsteeltubes4476
    @nationalsteeltubes44763 жыл бұрын

    U r explanation r very well sir 👌👌

  • @kulsumbanoo3595
    @kulsumbanoo35952 жыл бұрын

    Thank you sir your teaching very well

  • @riturathi6956
    @riturathi6956 Жыл бұрын

    Thanku so much sir Ji 👍🌹👍👍

  • @abhinandanjain2399
    @abhinandanjain2399 Жыл бұрын

    Thank you so much Gajendra sir.

  • @Dipak_22
    @Dipak_22 Жыл бұрын

    Happy Mathematics day sir I am join now today and today is international day 🤗so great day sir ❤️

  • @754rajni2
    @754rajni22 жыл бұрын

    Thanku so much sir 🙏🙏🙏

  • @priyankadadhich2116
    @priyankadadhich21163 жыл бұрын

    Thnku sir your vidio is very helpful for me

  • @santech-sanjeevkumar3254
    @santech-sanjeevkumar32542 жыл бұрын

    A lot of thanks sir 👌👌👌👌👌👌

  • @arnavlearningandgamingchan7630
    @arnavlearningandgamingchan76307 ай бұрын

    Thankyou so much sir 🌺

  • @gskerbecs9513
    @gskerbecs95138 ай бұрын

    Thanks A Lot sir

  • @Akhanda1107
    @Akhanda1107 Жыл бұрын

    Thanks sir. You are the best.

  • @adinathpangarkar1035
    @adinathpangarkar10353 жыл бұрын

    Thank you so much sir ❤️

  • @saumitragautam8333
    @saumitragautam83334 жыл бұрын

    Thank you.

  • @murshid37
    @murshid37 Жыл бұрын

    Bundle of thanks❤❤ ❤ ❤

  • @sudhanshusonare9936
    @sudhanshusonare99363 жыл бұрын

    Thank You so much sir 🙏🏻🙏🏻😊

  • @ARSk-gd1in
    @ARSk-gd1in3 жыл бұрын

    Thanks sir,I am really charmed

  • @ismritaneupane6828
    @ismritaneupane68282 жыл бұрын

    Thank you sir

  • @biswajitbarik1077
    @biswajitbarik10774 жыл бұрын

    Thank u for this sir

  • @mohdazahruddeen6398
    @mohdazahruddeen63983 жыл бұрын

    Sir your trick is unique

  • @shrejalgupta9520
    @shrejalgupta95202 жыл бұрын

    thankyou so much sir🤗🤗

  • @praveenranawat9119
    @praveenranawat91194 жыл бұрын

    Thanks guru ji

  • @Physicsguide_Surajsir
    @Physicsguide_Surajsir4 жыл бұрын

    गुरु पूर्णिमा पर्व की हार्दिक शुभकामनाये sir

  • @kshamashreekodandoor1711
    @kshamashreekodandoor17113 жыл бұрын

    Thank you so much sir😭 you saved mee🙏 i owe you

  • @mathematicians5925
    @mathematicians59252 жыл бұрын

    Thank you so much Sir 👍👍

  • @thebrokeartist1272
    @thebrokeartist12723 жыл бұрын

    Thank you very much sir 😊😊😊😊😊😊😊😊😊💖💖💖💖💖💓💓💓💓💓💓

  • @AnuSharma-rp4fp
    @AnuSharma-rp4fp4 жыл бұрын

    Nice video sir thank you

  • @user-jm4vp1nr8p
    @user-jm4vp1nr8p Жыл бұрын

    Thank you Respected sir

  • @kuchbhii_07
    @kuchbhii_07 Жыл бұрын

    ❤Sir i like your teaching method.

  • @narendraparmar1631
    @narendraparmar16315 ай бұрын

    Thanks Sir ji

  • @Terikehkelungaa-uj2yq
    @Terikehkelungaa-uj2yq2 жыл бұрын

    Sir aapke apke videos me bakwas nhi hota to dekhna faltu nhii lagta h🙏

  • @mitalgohil3022
    @mitalgohil30223 жыл бұрын

    World best sir for mathematics

  • @sd12217
    @sd122173 жыл бұрын

    What does (a,b,c,d) represent as it is not a coordinate ??

  • @anjalis1158
    @anjalis11584 жыл бұрын

    Thank you sir.

  • @padmakheechaudhury5039
    @padmakheechaudhury5039 Жыл бұрын

    Thanks a lot sir🙏

  • @Unknownkpopstaner22
    @Unknownkpopstaner222 жыл бұрын

    Hi sir i have a question. What exactly is a relation between unique solution and linear independence? If the matrix has a unique or one solution is it compulsory for all the vectors to be linearly independent?

  • @aniketmehtaiitmandi6278

    @aniketmehtaiitmandi6278

    2 жыл бұрын

    so to be more precise we are talking about homogeneous system of linear equations and in that case if det(A)=/=0 implies unique trivial solution which in turn implies Ai's(scalars) = 0 which implies linear independence of vectors of vector space So here homogeneous system is the key.

  • @AbdulWahab-ri7cd
    @AbdulWahab-ri7cd2 жыл бұрын

    Thank you so much 🥺🥺

  • @mathwithmurghoobahmedsyed7112
    @mathwithmurghoobahmedsyed71122 жыл бұрын

    Excellent

  • @amban2709
    @amban27094 жыл бұрын

    थैंक यू सो मच फ़ॉर डिस सर ग्रेट वर्क

  • @studylover6201
    @studylover62014 жыл бұрын

    Thanku sir .......🙏🙏

  • @satendrakashiyam771
    @satendrakashiyam7714 жыл бұрын

    Thank u so much sirji

  • @amalfatyma3365
    @amalfatyma33653 жыл бұрын

    very helpful video