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

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  • Опубліковано 22 гру 2024

КОМЕНТАРІ • 96

  • @GATEWallahbyPW
    @GATEWallahbyPW  2 роки тому +23

    Dear GATE Aspirants, Lecture notes, DPP, Video, and everything related to the class will be provided on the PW App. Inside the PW App, Gate Crash Course and Abhyas Batch for every class are created in the GATE category. There you can enroll in a free batch and access Videos, Notes, and DPPs.
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  • @edwardkenway7139
    @edwardkenway7139 10 місяців тому +44

    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 +30

    Topic starts at 5:50

  • @weird_a_weird
    @weird_a_weird 7 місяців тому +8

    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 6 місяців тому

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

    • @subrahmanyadheeraj5206
      @subrahmanyadheeraj5206 3 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 2 місяці тому

      Yes

  • @bhanudas3014
    @bhanudas3014 Рік тому +7

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

  • @GautamChouhan-h4q
    @GautamChouhan-h4q Рік тому +25

    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 ?

  • @LaxmiThakur_06
    @LaxmiThakur_06 8 днів тому +1

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

  • @SOULITUDE-xoxo
    @SOULITUDE-xoxo Рік тому +60

    Add timestamps

  • @asifrezak8366
    @asifrezak8366 10 місяців тому +3

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

  • @riyasikarwar788
    @riyasikarwar788 5 місяців тому +3

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

  • @SimranWatts-j6j
    @SimranWatts-j6j Місяць 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

  • @AyushPandey-i8j
    @AyushPandey-i8j Місяць 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...

  • @aashiii8017
    @aashiii8017 9 місяців тому

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

  • @saipatil4907
    @saipatil4907 4 місяці 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

  • @REKHASHARMA14
    @REKHASHARMA14 6 місяців тому

    Ur concepts are so clear

  • @Gurdassinghofficial
    @Gurdassinghofficial Рік тому +2

    26:35

  • @AyushansharadhyaAyushansharadh
    @AyushansharadhyaAyushansharadh Місяць тому

    Thank you sir ❤

  • @roshanchaudhary3390
    @roshanchaudhary3390 Рік тому

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

  • @Chirkut2511
    @Chirkut2511 13 днів тому

    45:54

  • @DeepaBatra-z2n
    @DeepaBatra-z2n 2 місяці тому +1

    Superb

    • @nitish.03
      @nitish.03 2 місяці тому

      How to download notes

  • @wildmonk604
    @wildmonk604 Рік тому

    Thank u sir for covering this topic

  • @techgamer4957
    @techgamer4957 9 місяців тому

    17:39
    1:04:40

    • @unknown09703
      @unknown09703 9 місяців тому

      Notes kaha hai pata hai ?

  • @shayariofashutoshkumarjha9360
    @shayariofashutoshkumarjha9360 2 роки тому +7

    Thank you sir for wonderful session.

  • @Sipra_Developer
    @Sipra_Developer 10 місяців тому

    2:00

  • @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 10 місяців тому

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

  • @Nay-z9m
    @Nay-z9m 3 місяці тому

    19:49

  • @vishalmishra1807
    @vishalmishra1807 Рік тому

    great sir

  • @REKHASHARMA14
    @REKHASHARMA14 6 місяців тому

    Thank u so much sir

  • @ankitsinha7502
    @ankitsinha7502 Рік тому +3

    thank you sir such a wonderful session,

  • @nitish.03
    @nitish.03 2 місяці тому

    How to download notes?

  • @livewithwisdom1
    @livewithwisdom1 Рік тому +1

    maja aagaya sir

  • @alimuddin2005
    @alimuddin2005 2 місяці тому

    1:12:49

  • @arnabdaw2587
    @arnabdaw2587 Рік тому +2

    thank u very much sir🙏🏻👍🏻

  • @SSCians-d3m
    @SSCians-d3m Рік тому

    Set of vector(vector space)

  • @shirisha3465
    @shirisha3465 11 місяців тому

    Sir it is use for IIT jam students also

  • @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

  • @continnum_radhe-radhe
    @continnum_radhe-radhe 5 місяців тому +1

    ❤❤❤

  • @musicclub1862
    @musicclub1862 Рік тому +2

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

  • @darshh.poetry2193
    @darshh.poetry2193 Рік тому

    very nice lectures

  • @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

  • @Interestingfacts00748
    @Interestingfacts00748 14 днів тому

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

  • @jausjva9977
    @jausjva9977 2 роки тому +1

    Thank you sir!!

  • @sudipsarkar1512
    @sudipsarkar1512 Рік тому +1

    Thank you sir ❤️

  • @sangharshravate
    @sangharshravate 3 місяці тому

    I think vector space is not for mechanical engineering syallabus

  • @Anjali-v2b7m
    @Anjali-v2b7m 3 місяці тому +1

    Is this only for gate

    • @NOTTY-GAMING.1M
      @NOTTY-GAMING.1M 2 місяці тому

      Any यूनिर्सिटी keliye nhi😢

  • @sudipsarkar1512
    @sudipsarkar1512 Рік тому +2

    47:00

  • @Motivationwallah-2
    @Motivationwallah-2 Рік тому

    Mai rgpv University se hu semester exam ke lie enaughf hai

  • @Abhi-z7q
    @Abhi-z7q Рік тому

    Yes

  • @nafeesalam7929
    @nafeesalam7929 Рік тому

    Thank ❤🌹 sir.

  • @nimishabajpai6816
    @nimishabajpai6816 2 роки тому +2

    Sir please start courses for ies also

  • @harshjain4041
    @harshjain4041 Рік 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

  • @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 Рік тому

      @@super.PY14 😂

  • @ashishchetry9636
    @ashishchetry9636 9 місяців тому +1

    Ayesha chhetri??

  • @Gunakar576
    @Gunakar576 Рік тому +1

    😅 thanks u sir

  • @sayanbiswas3885
    @sayanbiswas3885 Місяць тому

    Sir app bhi to single hoo 🙂

    • @jz2890
      @jz2890 Місяць тому

      Beti hai ek unki

  • @rathorgaurav8171
    @rathorgaurav8171 Рік тому

    Aap Ko man hi nahi karega ki lecture attend na karu

  • @ankush5308
    @ankush5308 Рік тому

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

  • @gojosatoru5464
    @gojosatoru5464 8 місяців тому +1

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

  • @PriyanshuKumar-gk7gc
    @PriyanshuKumar-gk7gc 7 місяців тому

    Who watched string advertisement... 😂

  • @vt6157
    @vt6157 Рік тому +5

    Bakvaas lecture

  • @arghadeepsaha5211
    @arghadeepsaha5211 8 місяців тому +42

    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 26 днів тому

    55:05

  • @RahulKumar-kc5lz
    @RahulKumar-kc5lz 25 днів тому

    1:50:00

  • @SayanChowdhuryOfficial
    @SayanChowdhuryOfficial Місяць 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