Was worried when I saw this was 56:57 mins long, but honestly this is the best explanation I've come across. Better than my lecturer and Khan Academy. Keep up the vids!
Thank you for the Extremely clear and slow paced explanation. My professor waffled about for on these 4 concepts for 2 weeks and I never could make heads or tails of her work. I hope your students acknowledge how lucky they are to have you.
I know this is an old vid, but you are such a life saver. I learned more from this vid than I learned from my professor, and it's really sad tbh. Thanks for this!
I am so grateful your explanation in details. it is so much helpful for preparing my final. i was confused many things when i learned it in classl. Thank you so much again.
haha was watchin this video before exam just for a recall xd its makes me laugh the way u describe everything. in a good way of course :) . comparing to my teacher u make it just so easy and smooth . we the people need this . big thanks man ,
Well explained but you made a minor error when finding the elements in the kernel. The last vector should be t [0 0 -2 0 1],but you have t [ 0 0 -2 0 2] . Since x5 = t and not 2t.
This video is perfect for dumb people like me. Haha, just kidding, but it's such an amazing video. Explanation - on point. Pace - On point. Examples - On point. Everything - On point.
ehhhhhh im stuck with Orthonormal Basis of image for a 4x4 matrix.... is it just following the steps to get the image and divide each of them by norm to get the orthonormal one?
The vectors in an orthonormal basis also have to be pairwise orthogonal. After you find a basis of the image of your matrix, you will need to apply the Gram-Schmidt Algorithm to transform your basis into an orthogonal one. Check out: th-cam.com/video/dCN7zzBBEwY/w-d-xo.html All that's left after is to normalize the vectors by dividing them by their respective norms.
So the section around 22:00, the method he uses to find the basis of the plane is - I thought - the method for finding the basis of the null space. Is that not correct?
I thought if there is any solution except 0,0,0 it is linearly dependent. here there is solution -6,1,0 why it is not linearly dependent? Also about dimension, I thought detention is 3 because there is 3 variables which are x,y,z
If the only solution is the zero solution, then the vectors are linearly independent. If there exists a nonzero solution, then the vectors are linearly dependent.
Yes.. there is nonzero solution which is -6,1,0 then it should be linearly dependent according to definition as you said, but you said that is linearly independent.
I followed everything that was done, but why is it done? The free variables confuse the hell out if me. I was under the impression that solving for n variables with less than n equations wasn't possible?
+Putins Cat Any homogeneous linear system with more variables than equations has infinitely many solutions. Consider the simple example x-y=0. The solutions to this equation are all the points on the line y=x.
slcmath@pc Sure, but what is with the r,s,t variables? I can replicate what was done, but why? When you multiple matrices, you take each row against a column vector, but then you can also take a matrix and split the columns into vectors and say cV1 + cV2 + cV3. I have no idea what that is about.. Is it just something that is what it is?
Was worried when I saw this was 56:57 mins long, but honestly this is the best explanation I've come across. Better than my lecturer and Khan Academy. Keep up the vids!
Thank you for the Extremely clear and slow paced explanation. My professor waffled about for on these 4 concepts for 2 weeks and I never could make heads or tails of her work. I hope your students acknowledge how lucky they are to have you.
with this video I understood what I couldn't 1 month now,thank you:)
This really helped clear up the fuzziness. Before all I could do was find explicit calculations. Now I feel confident in the concept.
Very clear and concise explanation of these concepts. Thank you!
very helpful, it would be nice if you add a table to contents so people can skip ahead to a section they need help with
I know this is an old vid, but you are such a life saver. I learned more from this vid than I learned from my professor, and it's really sad tbh. Thanks for this!
Glad you found it useful :-)
I am so grateful your explanation in details. it is so much helpful for preparing my final. i was confused many things when i learned it in classl. Thank you so much again.
Very clear and well explained
Thank you very much🙏
Your handwriting is perfect wow.
Damn, I didn't want to watch this at first, but I'm glad I did.
Perfect explanation
haha was watchin this video before exam just for a recall xd its makes me laugh the way u describe everything. in a good way of course :) . comparing to my teacher u make it just so easy and smooth .
we the people need this .
big thanks man ,
+Zoran Jovanov Totally agree with you.
Love this!!! So straight forward and easy to follow! Cannot thank you enough!!!
you make me so sleepy when I m watching this!
Thank you. Your explanation helped a lot and allowed me to take the leap to understand other videos and other parts of the algebra course
Thank you so much! Your video makes more sense than my prof's lecture.
Perfect. Life-saving.
I very much like the idea of saving a life. ;-)
best video on these concepts. Thanks
খুব ভালো লাগলো স্যার
Well explained but you made a minor error when finding the elements in the kernel. The last vector should be t [0 0 -2 0 1],but you have t [ 0 0 -2 0 2] . Since x5 = t and not 2t.
Aaron Geno You are absolutely right! Thank you for pointing this out.
44:18 for vector 3, variable 5. it's positive 1t not positive 2t. Unless I'm mistaken
Correct!
such a simple mistake and yet we all do it, every now and then. Thanks for the videos
I'm confused. I thought if there were degrees of free then the vectors were not linearly independent?
You rock! This is the best explanation, I've heard or seen.
thank you so much, I was not understanding it at all, but now ....
Really helpful video,thank you!
Very helpful and clear! Thank you and wish high mark in exam.
This video is perfect for dumb people like me. Haha,
just kidding, but it's such an amazing video.
Explanation - on point.
Pace - On point.
Examples - On point.
Everything - On point.
thank you! this helped me a lot!! text book is so confusing.
btw I like that you talk slow. not sleepy at all!
Thanks a lot man. Very well explained
Thank you for helping me understand, much appreciated, Stephen. :)
very nice teaching ad elaboration in deed thax very much
Incredibly helpful. Thank you.
45:21, V3 is not correct. It should be [0 0 2 0 -1] I guess.
Down to earth explanation..respect
Thank you so much for this video, it is so easy to understand!
had to watch it at speed 1.25
it is very lengthy, makes me uneasy
even though really deep explanation
thank you!
Best explanation bro,,keep it up
Thank you. Much appreciated
the tutorial is great, very helpful, thank you
ehhhhhh im stuck with Orthonormal Basis of image for a 4x4 matrix.... is it just following the steps to get the image and divide each of them by norm to get the orthonormal one?
The vectors in an orthonormal basis also have to be pairwise orthogonal. After you find a basis of the image of your matrix, you will need to apply the Gram-Schmidt Algorithm to transform your basis into an orthogonal one. Check out: th-cam.com/video/dCN7zzBBEwY/w-d-xo.html
All that's left after is to normalize the vectors by dividing them by their respective norms.
45:27 shouldnt the last element of v3 be 1 since you didnt scale it?
nice explanation, thank you !
good explanation...thank you ...
well done !!u helped us a lot!
you sound like a white khan academy
Haha! I will take that as a compliment ;-)
looool!
if sal khan didn't use his name for his videos and site i would assume he is white too
At 47:56, how do we put the vectors in a matrix [-3 41 0].. or [-3 2 0 0 0]
So the section around 22:00, the method he uses to find the basis of the plane is - I thought - the method for finding the basis of the null space. Is that not correct?
Both cases consist of finding solutions to a homogenous linear system.
Great job! Thanks!
lineal algebra
Thank you! Nice video.
nice explanation
That was great, thanks so much!
Thanks sir for this tutorial
thank you thank you so much ¡¡¡
thanks a lot , well explained
thank u that is well video
thanks great video
the last one should be 1 instead of 2 for the third column
I thought if there is any solution except 0,0,0 it is linearly dependent. here there is solution -6,1,0 why it is not linearly dependent? Also about dimension, I thought detention is 3 because there is 3 variables which are x,y,z
If the only solution is the zero solution, then the vectors are linearly independent.
If there exists a nonzero solution, then the vectors are linearly dependent.
Yes.. there is nonzero solution which is -6,1,0 then it should be linearly dependent according to definition as you said, but you said that is linearly independent.
Thx, clear enough
Thx
Thanks very much sir
well explained!
hellooo.
How do I determine the free variables of the system? at the minute 40:37
Variables that do not have a leading one in their column of the reduced matrix. ;-)
@@slcmathpc thanks! :)
I followed everything that was done, but why is it done? The free variables confuse the hell out if me. I was under the impression that solving for n variables with less than n equations wasn't possible?
+Putins Cat Any homogeneous linear system with more variables than equations has infinitely many solutions. Consider the simple example x-y=0. The solutions to this equation are all the points on the line y=x.
slcmath@pc Sure, but what is with the r,s,t variables? I can replicate what was done, but why? When you multiple matrices, you take each row against a column vector, but then you can also take a matrix and split the columns into vectors and say cV1 + cV2 + cV3. I have no idea what that is about.. Is it just something that is what it is?
thank you
thank youuuuuu
at 44:25, isn't X5 t = 1? not 2
The last entry of the third vector should indeed be 1.
thanks
its worth listening .. thank you..
THANK YOU :D
thank
You're really difficult to listen to in all honesty, but the explanation is good.
Thaaaaaaank you (:
ما افتهمت
thank you