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

[@GATEWallahbyPW]

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[@mathislove6138]

In 19:35 how the rank become 2

[@Mr.PlotPulse]

Row transformation se aata hai

[@edwardkenway7139]

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

[@toonstore1056]

Thanks yaar 😁

[@Rahul-et9oi]

47:05 linear span

[@sh1w5z]

Topic starts at 5:50

[@weird_a_weird]

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]

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

[@subrahmanyadheeraj5206]

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]

Yes

[@bhanudas3014]

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

[@LaxmiThakur_06]

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

[@GautamChouhan-h4q]

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 ?

[@SamarthPatel-208]

💯

[@SOULITUDE-xoxo]

Add timestamps

[@SimranWatts-j6j]

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

[@riyasikarwar788]

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

[@saipatil4907]

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

[@asifrezak8366]

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

[@REKHASHARMA14]

Ur concepts are so clear

[@AyushansharadhyaAyushansharadh]

Thank you sir ❤

[@AyushPandey-i8j]

[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...

[@wildmonk604]

Thank u sir for covering this topic

[@roshanchaudhary3390]

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

[@DeepaBatra-z2n]

Superb

[@nitish.03]

How to download notes

[@shayariofashutoshkumarjha9360]

Thank you sir for wonderful session.

[@annafiufoundation3702]

45:01, 55:01

[@aashiii8017]

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

[@ashishchetry9636]

Ayesha chhetri?

[@Gurdassinghofficial]

26:35

[@ankitsinha7502]

thank you sir such a wonderful session,

[@livewithwisdom1]

maja aagaya sir

[@Interestingfacts00748]

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

[@SSCians-d3m]

Set of vector(vector space)

[@vishalmishra1807]

great sir

[@Gurdassinghofficial]

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

[@chitranshdubey5225]

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

[@ByAnIndian2001]

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

[@yessubharv1400]

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

[@REKHASHARMA14]

Thank u so much sir

[@Chirkut2511]

45:54

[@arnabdaw2587]

thank u very much sir🙏🏻👍🏻

[@techgamer4957]

17:39 1:04:40

[@unknown09703]

Notes kaha hai pata hai ?

[@shirisha3465]

Sir it is use for IIT jam students also

[@soham2249]

No

[@Nay-z9m]

19:49

[@Motivationwallah-2]

Mai rgpv University se hu semester exam ke lie enaughf hai

[@darshh.poetry2193]

very nice lectures

[@Sipra_Developer]

2:00

[@jausjva9977]

Thank you sir!!

[@alimuddin2005]

1:12:49

[@sudipsarkar1512]

Thank you sir ❤️

[@msalam4912]

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

[@PrabhatPandey15]

Ye physics wallah chhod chuke hai

[@continnum_radhe-radhe]

❤❤❤

[@souravbhagat1358]

Sir pls next Topic Calculus: Start kra dhijye .

[@inferno2927]

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

[@Rohit_roy__]

@@inferno2927 🤣🤣🤣

[@me_suman_raj]

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

[@Mohitchoudhary_2381]

​@@inferno2927ha

[@sangharshravate]

I think vector space is not for mechanical engineering syallabus

[@nitish.03]

How to download notes?

[@musicclub1862]

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

[@nafeesalam7929]

Thank ❤🌹 sir.

[@sudipsarkar1512]

47:00

[@nimishabajpai6816]

Sir please start courses for ies also

[@Anjali-v2b7m]

Is this only for gate

[@NOTTY-GAMING.1M]

Any यूनिर्सिटी keliye nhi😢

[@ashishchetry9636]

Ayesha chhetri??

[@ultimater1538]

aasiess chhetri

[@Abhi-z7q]

Yes

[@Abhi-z7q]

Yes sir

[@Gunakar576]

😅 thanks u sir

[@sayanbiswas3885]

Sir app bhi to single hoo 🙂

[@jz2890]

Beti hai ek unki

[@harshjain4041]

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

[@Scolar69]

Bro give exam its better

[@rishabhpandey12aroll7.5]

gareeb bsdk

[@rathorgaurav8171]

Aap Ko man hi nahi karega ki lecture attend na karu

[@VinayKumar-bn1pc]

Sir iska pdf kha se milega .,..

[@super.PY14]

lik le bhai , maths ka pdf se na hona kuch

[@SiddlovesIT]

@@super.PY14 😂

[@gojosatoru5464]

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

[@SaiAbitathaDUCIC]

hold my cup of tea 😉😉

[@ankush5308]

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

[@PriyanshuKumar-gk7gc]

Who watched string advertisement... 😂

[@vt6157]

Bakvaas lecture

[@arghadeepsaha5211]

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.

[@nothingyoutube1]

Thanks bro❤

[@AutoMarathi-qd7dd]

धन्यवाद ❤

[@RahulKumar-kc5lz]

55:05

[@RahulKumar-kc5lz]

1:50:00

[@SayanChowdhuryOfficial]

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