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. 👉PW App link: bit.ly/GATE_PW 🌐 GATE Wallah - ME, CE & XE - ua-cam.com/channels/Grrw9x3_B_fItUIBMvqAUw.html 🌐 GATE Wallah - EE, EC & CS - ua-cam.com/channels/uGWIkiNaWjsCqybgxGuxfg.html ▶ Our Telegram Page: t.me/gatewallah_official ▶ Telegram Group for Electronics & Communication Engineering : t.me/GWElectroandcom ▶ Telegram Group for Computer Science and Information Technology Engineering : t.me/Gwcomsciandinfo ▶ Telegram Group for Mechanical Engineering : t.me/GATEWallahMechanicalengineering ▶ Telegram Group for Civil Engineering : t.me/GATEWallahCivilEngineering ▶ Missed Call Number for GATE Related Enquiry : 08069458181 ▶ Our Instagram Page : bit.ly/Insta_GATE Dear GATE Aspirants, Any irrelevant/abusive comment will not be tolerated, students doing so will be blocked immediately
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
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)
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 \( \mathbb{R}^3 \).
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
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 ?
[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...
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.
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
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.
👉PW App link: bit.ly/GATE_PW
🌐 GATE Wallah - ME, CE & XE - ua-cam.com/channels/Grrw9x3_B_fItUIBMvqAUw.html
🌐 GATE Wallah - EE, EC & CS - ua-cam.com/channels/uGWIkiNaWjsCqybgxGuxfg.html
▶ Our Telegram Page: t.me/gatewallah_official
▶ Telegram Group for Electronics & Communication Engineering : t.me/GWElectroandcom
▶ Telegram Group for Computer Science and Information Technology Engineering : t.me/Gwcomsciandinfo
▶ Telegram Group for Mechanical Engineering : t.me/GATEWallahMechanicalengineering
▶ Telegram Group for Civil Engineering : t.me/GATEWallahCivilEngineering
▶ Missed Call Number for GATE Related Enquiry : 08069458181
▶ Our Instagram Page : bit.ly/Insta_GATE
Dear GATE Aspirants, Any irrelevant/abusive comment will not be tolerated, students doing so will be blocked immediately
In 19:35 how the rank become 2
Row transformation se aata hai
Sir yr handsome 😊
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
Thanks yaar 😁
47:05 linear span
Topic starts at 5:50
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)
and also in 39.50 S2 is neither a vector space nor vector subspace of S1
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 \( \mathbb{R}^3 \).
Yes
Thanks so much sir and your writing is amazing easy understandable .....
i usually do not prefer commenting but i really like your way of teaching
Add timestamps
The way sir says "thik he, perfect, perfect"😧✨❤️
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
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 ?
💯
Sir there are 8 conditions which needs to be followed by the vectors in vectorspace .
[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...
I think your method of teaching is excellent, i really enjoy watching you at 1.5x
45:01, 55:01
47:34 span
vector space, linear span, Basis CSE ke syllabus me hai ?
56:30 X is maharathi kyuki vo akela hi kaafi h...
Ur concepts are so clear
Thank you sir for wonderful session.
Thank u sir for covering this topic
thank you sir such a wonderful session,
26:35
Thank you sir ❤
17:39
1:04:40
Notes kaha hai pata hai ?
Superb
How to download notes
thank u very much sir🙏🏻👍🏻
this video is only for gate aspirants not more valuable for BTech 1st year
at 14:02 shouldnt X3 be the transpose of the matrix too like X1 and X2
Ayesha chhetri?
सर मुझे आपका क्लास कैसे मिलेगा या वीडियो क्योंकि मैं फिजिक्स वाला पर भी गया था उसमें आपका वीडियो नहीं दिखा
Ye physics wallah chhod chuke hai
19:49
Sir, First question mein
|A| = 0
Keu huya....? Please reply anyone😊....
Highest order minor zero h iss liye |A|=0
hua
@@chitranshdubey5225 uske baad lambda=5/14 keise??
Rank max se km hone k liye min ek row or column zero hona chahiye nd us case me determinant zero ho jayega
45:54
Ece branch h y video dekhh sktt h ky????
Sir it is use for IIT jam students also
No
Thank u so much sir
Sir mdu university ka liya bhe pad sakta ha
very nice lectures
Set of vector(vector space)
great sir
nice
Sir pls next Topic Calculus: Start kra dhijye .
bhai joh chl rha h woh ache se aata h kya ?
@@inferno2927 🤣🤣🤣
Beta jo padhaya hu wo ache se aata hai kya😅... Sir be like.. Ja phle ja Kr DPP solve kar tu😅
@@inferno2927ha
maja aagaya sir
Sir please start courses for ies also
2:00
Thank you sir ❤️
Thank you sir!!
47:00
Is this only for gate
Any यूनिर्सिटी keliye nhi😢
Mai rgpv University se hu semester exam ke lie enaughf hai
How to download notes?
1:12:49
I think vector space is not for mechanical engineering syallabus
❤❤❤
Thank ❤🌹 sir.
Nhii
Ayesha chhetri??
aasiess chhetri
Yes
Yes sir
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
Bro give exam its better
gareeb bsdk
Aap Ko man hi nahi karega ki lecture attend na karu
Sir iska pdf kha se milega .,..
lik le bhai , maths ka pdf se na hona kuch
@@super.PY14 😂
😅 thanks u sir
Sir app bhi to single hoo 🙂
Beti hai ek unki
Sir please class ke baad revision ke liye pdf bhi add kar diya kare 😭😭😁
Bakvaas lecture
Who watched string advertisement... 😂
2027 GATE AIR-1 CHAKRISH!!!
TAKE IT IN WRITTEN
hold my cup of tea 😉😉
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.
Thanks bro❤
धन्यवाद ❤
1:50:00
55:05
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