Engineering Mathematics 12 | Linear Span, Basis, Dimensions | GATE All Branches

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  • Опубліковано 1 лют 2025

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  • @GATEWallahbyPW
    @GATEWallahbyPW  2 роки тому +25

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  • @edwardkenway7139
    @edwardkenway7139 Рік тому +55

    13:46 Linear Span, Basis, Dimensions
    27:32 Vector space is a set of vectors with real values
    41:18 Vector spaces are sets of vectors having certain common properties
    55:04 Linear span represents the set of linear combinations of vectors in a vector space.
    1:08:50 Explained the concept of linear span and its relation to basis and dimensions
    1:22:36 Method 2 explains linear span through system of non-homogeneous equations.
    1:36:22 Solution exists with trivial or non-trivial values of c1 and c2
    1:50:01 Linear dependency should always be uniform, either two columns or one

  • @sh1w5z
    @sh1w5z Рік тому +35

    Topic starts at 5:50

  • @weird_a_weird
    @weird_a_weird 8 місяців тому +11

    38:33 W is not a subspace of V (0 vector is not there in W, sum of 2 vectors in W doesn't give a vector belonging to W , scalar multiple of any vector of W doesn't belong to W)

    • @PRIYANKAADHIKARI-xv4gm
      @PRIYANKAADHIKARI-xv4gm 8 місяців тому

      and also in 39.50 S2 is neither a vector space nor vector subspace of S1

    • @subrahmanyadheeraj5206
      @subrahmanyadheeraj5206 4 місяці тому

      yes bro
      To determine if \( W = \{(1, 2, 1), (1, 1, 1)\} \) is a subspace of the vector space \( V = \mathbb{R}^3 \), we need to check if \( W \) satisfies the following conditions for being a subspace:
      1. **The zero vector is in \( W \)**: A subspace must contain the zero vector \( (0, 0, 0) \).

      2. **Closed under addition**: If \( \mathbf{u}, \mathbf{v} \in W \), then \( \mathbf{u} + \mathbf{v} \in W \).
      3. **Closed under scalar multiplication**: If \( \mathbf{u} \in W \) and \( c \) is any scalar, then \( c\mathbf{u} \in W \).
      Let's analyze this step by step.
      ### 1. Check if the zero vector is in \( W \)
      The set \( W = \{(1, 2, 1), (1, 1, 1)\} \) does not explicitly contain the zero vector. Therefore, \( W \) does **not** contain the zero vector.
      ### 2. Check closure under addition
      Let's add the two vectors in \( W \):
      \[
      (1, 2, 1) + (1, 1, 1) = (2, 3, 2)
      \]
      The result \( (2, 3, 2) \) is not in \( W \), so \( W \) is not closed under addition.
      ### 3. Check closure under scalar multiplication
      Let's multiply \( (1, 2, 1) \) by a scalar, say \( c = 2 \):
      \[
      2 \cdot (1, 2, 1) = (2, 4, 2)
      \]
      Since \( (2, 4, 2) \) is not in \( W \), \( W \) is not closed under scalar multiplication.
      ### Conclusion
      Since \( W \) does not satisfy the required conditions (it does not contain the zero vector, and it is not closed under addition and scalar multiplication), \( W \) is **not** a subspace of \( \mathbb{R}^3 \).

    • @vikaskummari5641
      @vikaskummari5641 4 місяці тому

      Yes

  • @bhanudas3014
    @bhanudas3014 Рік тому +7

    Thanks so much sir and your writing is amazing easy understandable .....

  • @LaxmiThakur_06
    @LaxmiThakur_06 Місяць тому +2

    i usually do not prefer commenting but i really like your way of teaching

  • @SOULITUDE-xoxo
    @SOULITUDE-xoxo Рік тому +65

    Add timestamps

  • @Kanha_gaming999
    @Kanha_gaming999 24 дні тому

    The way sir says "thik he, perfect, perfect"😧✨❤️

  • @SimranWatts-j6j
    @SimranWatts-j6j 2 місяці тому +1

    sir in last ques variables will be 2 that is c1 and c2 if we will go through method 2 and rank is also 2 so there is unique solution instead of infinitely solution like my comment if u r agree

  • @GautamChouhan-h4q
    @GautamChouhan-h4q Рік тому +28

    how he simply explains vector space and subspace , there is 8 condition to be vector space and for subspace it follow 2 rule with having origin in subspace ?

  • @riyasikarwar788
    @riyasikarwar788 7 місяців тому +3

    Sir there are 8 conditions which needs to be followed by the vectors in vectorspace .

  • @AyushPandey-i8j
    @AyushPandey-i8j 3 місяці тому +1

    [1].I have seen this lecture today.I have completely understood all the concepts you explained in class. Your teaching method was very simple and effective, which made me understand everything easily. I am very grateful to you for your guidance and hard work. Your student, [Ayush ]...🫡❤️
    1ST NOVEMBER 2024...

  • @saipatil4907
    @saipatil4907 6 місяців тому

    I think your method of teaching is excellent, i really enjoy watching you at 1.5x

  • @annafiufoundation3702
    @annafiufoundation3702 Рік тому +2

    45:01, 55:01

  • @AryanPatel-l2e
    @AryanPatel-l2e Місяць тому +1

    47:34 span

  • @asifrezak8366
    @asifrezak8366 11 місяців тому +3

    vector space, linear span, Basis CSE ke syllabus me hai ?

  • @roshanchaudhary3390
    @roshanchaudhary3390 Рік тому

    56:30 X is maharathi kyuki vo akela hi kaafi h...

  • @REKHASHARMA14
    @REKHASHARMA14 7 місяців тому

    Ur concepts are so clear

  • @shayariofashutoshkumarjha9360
    @shayariofashutoshkumarjha9360 2 роки тому +7

    Thank you sir for wonderful session.

  • @wildmonk604
    @wildmonk604 Рік тому

    Thank u sir for covering this topic

  • @ankitsinha7502
    @ankitsinha7502 2 роки тому +3

    thank you sir such a wonderful session,

  • @Gurdassinghofficial
    @Gurdassinghofficial Рік тому +2

    26:35

  • @AyushansharadhyaAyushansharadh
    @AyushansharadhyaAyushansharadh 2 місяці тому

    Thank you sir ❤

  • @techgamer4957
    @techgamer4957 11 місяців тому

    17:39
    1:04:40

    • @unknown09703
      @unknown09703 10 місяців тому

      Notes kaha hai pata hai ?

  • @DeepaBatra-z2n
    @DeepaBatra-z2n 4 місяці тому +2

    Superb

    • @nitish.03
      @nitish.03 4 місяці тому

      How to download notes

  • @arnabdaw2587
    @arnabdaw2587 Рік тому +2

    thank u very much sir🙏🏻👍🏻

  • @Interestingfacts00748
    @Interestingfacts00748 Місяць тому +1

    this video is only for gate aspirants not more valuable for BTech 1st year

  • @aashiii8017
    @aashiii8017 11 місяців тому

    at 14:02 shouldnt X3 be the transpose of the matrix too like X1 and X2

  • @msalam4912
    @msalam4912 Рік тому

    सर मुझे आपका क्लास कैसे मिलेगा या वीडियो क्योंकि मैं फिजिक्स वाला पर भी गया था उसमें आपका वीडियो नहीं दिखा

  • @Nay-z9m
    @Nay-z9m 4 місяці тому

    19:49

  • @Gurdassinghofficial
    @Gurdassinghofficial Рік тому +2

    Sir, First question mein
    |A| = 0
    Keu huya....? Please reply anyone😊....

    • @chitranshdubey5225
      @chitranshdubey5225 Рік тому +4

      Highest order minor zero h iss liye |A|=0
      hua

    • @ByAnIndian2001
      @ByAnIndian2001 Рік тому

      @@chitranshdubey5225 uske baad lambda=5/14 keise??

    • @yessubharv1400
      @yessubharv1400 Рік тому

      Rank max se km hone k liye min ek row or column zero hona chahiye nd us case me determinant zero ho jayega

  • @Chirkut2511
    @Chirkut2511 Місяць тому

    45:54

  • @musicclub1862
    @musicclub1862 Рік тому +2

    Ece branch h y video dekhh sktt h ky????

  • @shirisha3465
    @shirisha3465 Рік тому

    Sir it is use for IIT jam students also

  • @REKHASHARMA14
    @REKHASHARMA14 7 місяців тому

    Thank u so much sir

  • @pankajtiwal
    @pankajtiwal 15 днів тому

    Sir mdu university ka liya bhe pad sakta ha

  • @darshh.poetry2193
    @darshh.poetry2193 Рік тому

    very nice lectures

  • @SSCians-d3m
    @SSCians-d3m Рік тому

    Set of vector(vector space)

  • @vishalmishra1807
    @vishalmishra1807 Рік тому

    great sir

  • @Engineering_Drawing_Classes
    @Engineering_Drawing_Classes 16 днів тому

    nice

  • @souravbhagat1358
    @souravbhagat1358 2 роки тому +10

    Sir pls next Topic Calculus: Start kra dhijye .

    • @inferno2927
      @inferno2927 2 роки тому +1

      bhai joh chl rha h woh ache se aata h kya ?

    • @Rohit_roy__
      @Rohit_roy__ 2 роки тому

      @@inferno2927 🤣🤣🤣

    • @me_suman_raj
      @me_suman_raj 2 роки тому

      Beta jo padhaya hu wo ache se aata hai kya😅... Sir be like.. Ja phle ja Kr DPP solve kar tu😅

    • @Mohitchoudhary_2381
      @Mohitchoudhary_2381 Рік тому

      ​@@inferno2927ha

  • @livewithwisdom1
    @livewithwisdom1 Рік тому +1

    maja aagaya sir

  • @nimishabajpai6816
    @nimishabajpai6816 2 роки тому +2

    Sir please start courses for ies also

  • @Sipra_Developer
    @Sipra_Developer 11 місяців тому

    2:00

  • @sudipsarkar1512
    @sudipsarkar1512 2 роки тому +1

    Thank you sir ❤️

  • @jausjva9977
    @jausjva9977 2 роки тому +1

    Thank you sir!!

  • @sudipsarkar1512
    @sudipsarkar1512 2 роки тому +2

    47:00

  • @Anjali-v2b7m
    @Anjali-v2b7m 4 місяці тому +1

    Is this only for gate

    • @NOTTY-GAMING.1M
      @NOTTY-GAMING.1M 3 місяці тому

      Any यूनिर्सिटी keliye nhi😢

  • @Motivationwallah-2
    @Motivationwallah-2 Рік тому

    Mai rgpv University se hu semester exam ke lie enaughf hai

  • @nitish.03
    @nitish.03 4 місяці тому

    How to download notes?

  • @alimuddin2005
    @alimuddin2005 4 місяці тому

    1:12:49

  • @sangharshravate
    @sangharshravate 5 місяців тому

    I think vector space is not for mechanical engineering syallabus

  • @continnum_radhe-radhe
    @continnum_radhe-radhe 7 місяців тому +1

    ❤❤❤

  • @nafeesalam7929
    @nafeesalam7929 2 роки тому

    Thank ❤🌹 sir.

  • @AdityaPanwar-r2e
    @AdityaPanwar-r2e Місяць тому

    Nhii

  • @ashishchetry9636
    @ashishchetry9636 11 місяців тому +1

    Ayesha chhetri??

  • @Abhi-z7q
    @Abhi-z7q Рік тому

    Yes

  • @harshjain4041
    @harshjain4041 2 роки тому +2

    hey i have already appeared in 6lpa and also selected the slot in this 4lpa hiring process so should i appear in exam or not ? *coz selected slot

  • @rathorgaurav8171
    @rathorgaurav8171 Рік тому

    Aap Ko man hi nahi karega ki lecture attend na karu

  • @VinayKumar-bn1pc
    @VinayKumar-bn1pc 2 роки тому +1

    Sir iska pdf kha se milega .,..

    • @super.PY14
      @super.PY14 2 роки тому +1

      lik le bhai , maths ka pdf se na hona kuch

    • @SiddlovesIT
      @SiddlovesIT 2 роки тому

      @@super.PY14 😂

  • @Gunakar576
    @Gunakar576 Рік тому +1

    😅 thanks u sir

  • @sayanbiswas3885
    @sayanbiswas3885 3 місяці тому

    Sir app bhi to single hoo 🙂

    • @jz2890
      @jz2890 3 місяці тому +1

      Beti hai ek unki

  • @ankush5308
    @ankush5308 2 роки тому

    Sir please class ke baad revision ke liye pdf bhi add kar diya kare 😭😭😁

  • @vt6157
    @vt6157 Рік тому +5

    Bakvaas lecture

  • @PriyanshuKumar-gk7gc
    @PriyanshuKumar-gk7gc 9 місяців тому

    Who watched string advertisement... 😂

  • @gojosatoru5464
    @gojosatoru5464 10 місяців тому +1

    2027 GATE AIR-1 CHAKRISH!!!
    TAKE IT IN WRITTEN

  • @arghadeepsaha5211
    @arghadeepsaha5211 9 місяців тому +41

    13:46 Linear Span, Basis, Dimensions
    27:32 Vector space is a set of vectors with real values
    41:18 Vector spaces are sets of vectors having certain common properties
    55:04 Linear span represents the set of linear combinations of vectors in a vector space.
    1:08:50 Explained the concept of linear span and its relation to basis and dimensions
    1:22:36 Method 2 explains linear span through system of non-homogeneous equations.
    1:36:22 Solution exists with trivial or non-trivial values of c1 and c2
    1:50:01 Linear dependency should always be uniform, either two columns or one.

  • @RahulKumar-kc5lz
    @RahulKumar-kc5lz 2 місяці тому

    1:50:00

  • @RahulKumar-kc5lz
    @RahulKumar-kc5lz 2 місяці тому

    55:05

  • @SayanChowdhuryOfficial
    @SayanChowdhuryOfficial 3 місяці тому

    13:46 Linear Span, Basis, Dimensions
    27:32 Vector space is a set of vectors with real values
    41:18 Vector spaces are sets of vectors having certain common properties
    55:04 Linear span represents the set of linear combinations of vectors in a vector space.
    1:08:50 Explained the concept of linear span and its relation to basis and dimensions
    1:22:36 Method 2 explains linear span through system of non-homogeneous equations.
    1:36:22 Solution exists with trivial or non-trivial values of c1 and c2
    1:50:01 Linear dependency should always be uniform, either two columns or one