Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (540+ videos) you might find helpful. Thanks much, Adam
Glad I could help; hope the exam went well! Make sure to check out my website adampanagos.org where I have a lot of other resources available that you might find helpful. Thanks, Adam
Ah yes, great catch! I guess I got a little carried away with the zeros there. =) Definitely should only be 4, not 5. Thanks for noting and glad you like the videos. Adam
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
Thanks for the kind words! If you found the video useful make sure to check out my website adampanagos.org where I have a lot of other resources available and consider supporting development of new videos through www.patreon.com/agpanagos. Thanks! Adam
Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam
My favorite linear algebra text for undergraduates at the moment is www.amazon.com/Linear-Algebra-Its-Applications-5th/dp/032198238X. Hope that helps. Adam
Just love your teaching videos, Adam!!! I’m a math teacher too, I’m wondering what software / app you’re using in your explanation? It looks so smooth during your teaching!! May I know it ? Thank you very much . 🙏
For most of my videos, I use Doceri (an app for my iPad, apps.apple.com/us/app/doceri-remote/id412443803?ls=1) that lets me pre-record all the writing. Then, I can "play back" the writing while I record the audio. It’s a very useful tool for me. Hope that helps, Adam
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
Yes, you're correct at that time instant. Note that a few seconds later I caught the mistake while recording and got things corrected. Sorry for the mistake. Good catch!
You’re welcome, thanks for watching. Make sure to check out my website adampanagos.org where I have additional resources you might find useful, and consider supporting development of new videos through www.patreon.com/agpanagos. Thanks! Adam
The dimension of any space is always equal to the number of basis vectors it takes to represent the space. In this case, we have 3 basis vectors that were found. So, the dimension of the null space is 3. In general, if you need N basis vectors, you have an N-dimensional space. Hope that helps, Adam
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (395+ videos) you might find helpful. Thanks, Adam.
how do you have 3 vectors with only a geometric multiplicity of 2? I thought the number of vectors you need to have needs to equal the nullity of the reduced matrix
I'm not sure if I follow how "geometric multiplicity" has anything to do with this. As shown in the video, the original matrix A is row equivalent to matrix B which has just 2 pivots. Since there are 5 columns, then there are 5 - 2 = 3 free variables which correspond to the 3 vectors that form the basis for the null space; e.g. x1 and x2 can be written in terms of x3, x4, and x5.
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
Yes. This is literally exactly what I needed.
Glad I could help, thanks for watching!
This is the clearest explanation on this subject I have seen thus far! Thank you!
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (540+ videos) you might find helpful. Thanks much, Adam
Great...after 2 hrs i have exam...this helped a lot easy explanation...thanks a lot...
Glad I could help; hope the exam went well! Make sure to check out my website adampanagos.org where I have a lot of other resources available that you might find helpful. Thanks,
Adam
Sorry, at timestamp 4:43. Multiplying A by = . Correct? Forgot to mention that your Linear Algebra videos are by far the best!!
Ah yes, great catch! I guess I got a little carried away with the zeros there. =) Definitely should only be 4, not 5. Thanks for noting and glad you like the videos.
Adam
These videos are some of the best linear algebra content avialable on the internet
Thank you for the kind words!
thanks a lot sir, you are better than my teacher at my university.
Thanks for the kind words, glad I was able to help! Best,
Adam
9 minutes of this video is better than 4hours worth of lectures in university
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
Cleared every doubt .
Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam
You are a blessing and a great teacher
Thanks!
Perfectly explained! Exactly what I needed.
thank you a lot sir. You make it easy for student to understand.
Glad I could help, thanks for watching!
great explanation sir...
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
I learned what nullspace and dimension is in 9 min than I did in 1 week lol, excellent video!
Awesome! Glad I could help. Thanks!
amazing teacher really helped thanks
Glad I could help, thanks for watching! Check out my website adampanagos.org where I have about 400+ videos you might find helpful.
Excellent Explanation.
Keep up good work.
Thanks
Surya
Thanks for the kind words! If you found the video useful make sure to check out my website adampanagos.org where I have a lot of other resources available and consider supporting development of new videos through www.patreon.com/agpanagos. Thanks!
Adam
I appreciate you filling in the missing steps from my math notes
Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content you might find helpful. Thanks, Adam
Great teacher indeed...this video eradicated my confusion on this topic...thank you
Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam
Thank you so much. It was of great help. Could you please recommend some reference books on this topic?
My favorite linear algebra text for undergraduates at the moment is www.amazon.com/Linear-Algebra-Its-Applications-5th/dp/032198238X. Hope that helps.
Adam
You are a blessing and a great teacher. tnx a lot
Thanks!
Just love your teaching videos, Adam!!! I’m a math teacher too, I’m wondering what software / app you’re using in your explanation? It looks so smooth during your teaching!! May I know it ? Thank you very much . 🙏
For most of my videos, I use Doceri (an app for my iPad, apps.apple.com/us/app/doceri-remote/id412443803?ls=1) that lets me pre-record all the writing. Then, I can "play back" the writing while I record the audio. It’s a very useful tool for me. Hope that helps,
Adam
@@AdamPanagos thank you so much, Adam!!!👍👍
great video, very clear explanation. thanks!
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
thanks a lot!! great explanation
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
Are the vectors we have at the end (in this case, 3 vectors) always linearly independent? They have to be if they make the basis of the null space.
Yes, using this approach they will be.
if there is no free variable so if all row has pivot what will we do what is the dimension of nullspace
you are great, thank you
At time stamp 06:53, X3 for the 3rd row and 1st column should be 1 not 0..??
Yes, you're correct at that time instant. Note that a few seconds later I caught the mistake while recording and got things corrected. Sorry for the mistake. Good catch!
Do we need to check whether these 3 vectors are linearly independent?
Great video! Thanks for posting.
(At 4:43, shouldn't the zero vector have only 4 elements?)
nope, it has the same number of elements as the number of columns
@@Therysin why though a 4x5 matrix X 5x1 = 4x1 no?
@@jerrerock idk man, it's been two years. I got my engineering degree now lol
Thank you so much!!! 💚
You’re welcome, thanks for watching. Make sure to check out my website adampanagos.org where I have additional resources you might find useful, and consider supporting development of new videos through www.patreon.com/agpanagos. Thanks!
Adam
I thought the vectors must also be linearly independent to form a basis?
Either definition is used. Some texts/resources require independence of the vectors, others just require spanning. Hope that helps.
Adam
Thank you so much
It's help me a lot
You're welcome, glad I could help.
Can anyone please explain 8:30 to 8:40 ??? Please
The dimension of any space is always equal to the number of basis vectors it takes to represent the space. In this case, we have 3 basis vectors that were found. So, the dimension of the null space is 3. In general, if you need N basis vectors, you have an N-dimensional space. Hope that helps,
Adam
@@AdamPanagos okay!! Thanks
thank u so much
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (395+ videos) you might find helpful. Thanks, Adam.
You are my senior
What if you can't write your basic variables with your free variables. Meaning I have a basic variable with other free variables?
You can always write your basic variables as a function of your free variables.
how do you have 3 vectors with only a geometric multiplicity of 2? I thought the number of vectors you need to have needs to equal the nullity of the reduced matrix
I'm not sure if I follow how "geometric multiplicity" has anything to do with this.
As shown in the video, the original matrix A is row equivalent to matrix B which has just 2 pivots. Since there are 5 columns, then there are 5 - 2 = 3 free variables which correspond to the 3 vectors that form the basis for the null space; e.g. x1 and x2 can be written in terms of x3, x4, and x5.
brilliant !!!! :)
Thanks and thanks for watching. Best,
Adam
I think your zero matrix should have only 4 zeroes instead of 5.
What zero matrix? Can you tell me what time in the video you're referring to?
thank you for this
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.