Dimension of the null space or nullity | Vectors and spaces | Linear Algebra | Khan Academy
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- Опубликовано: 21 янв 2025
- Dimension of the Null Space or Nullity
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11:40 for Dimension of Null space, you're welcome
skipped whole 6 month classes watch all videos . passed
This guys is the best. But let's face it if universities and colleges could hire professors like this guy who can "teach" a concept and "explain" thoroughly then people would not even have to resort to watching his videos as last minute life savers before a test or exam. Just because someone has a PHD in a subject does not necessarily mean they can teach it. They might be a complete expert and genius in that subject but getting other people to learn it and teaching it to them is a completely different story. The institutes should look at Khan's videos as an example how a great teacher should explain concepts and questions to someone rather than looking at whether they have got a PHD or doctorate in a course.
A lot of those teachers with PhDs are being paid by the college to do research, teaching is their secondary profession. Research brings in big money in grants and publicity to the universities, so they hire smart people who can conduct research
Haha, didn't think I'd be returning to a 3 year old comment. To be honest, I am also to blame for my lack of incompetence. I procrastinated and would even skip some classes which led to me being in a state where I would have to watch these last minute videos online. I still stand by what I said back then though. treasy brought up a good point a lot of profs are actually at institutions for research as their primary job. I had one prof who's lectures were pretty meaningless, but he had contributed a truck load to the university's research.
I wrote that comment because I was just really frustrated and was just venting when I should have been studying LOL
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Not just vaguely useful, EXTREMELY useful.
Why can't every lecturer explain as clearly and simply as this?
don't u think thats like asking, why cant every basketball player shoot free throws.....
Vaguely useful? are you kidding me, thus was great! Thanks for the help Sal!
Love you Sal. Your videos make me look like some sort of super genius in class!
I come listen to this guys voice and all my stress about up coming exam goes away.
thank you very much sir , i have final exam in this after one hour
you really explained everything for me better than that one we called prof in our college
faisal alfaisal
كيف كان الامتحان 😂
You make it so clear. Thank you
Thanks guy you just saved me from my mid-term!
Amazing job, trying to get ready for linear algebra exam tomorrow.
wadiczka How’d it go? Lol
God bless you! The tutorial was amazing!
Thanks so much, this is EXACTLY what i needed! :D
Jesus christ that ending "Anyway hope you found that, vaguely useful" LOL
absolutely amazing!!! u are a genius, thanks sooooo much
Khan for president!!!! 2022
Sorry in the last and video you said that the pivot columns make a basis but in this one you say that the free variable columns make a basis. But both usually have different dimension. How does that work? Thanks
Thank you so much. I love your explanation.
Dude, awesome.
A thank you would not be enough . . . I dont know wat to say
God Bless You
Hi there, I would like to know if I did exactly like you did in the video, except I put in row echelon form instead of a row reduced echelon form. Would I still be able to get the right answer?
Doesn't this mean that the dimension of A is equal to the number of collumns minus the number of rows of A. Since the reduced row echelon form will allways contain a number of pivots equal to the number of rows?
verrryyyy verryy useful ！！！！！！
thanks it helps a lot
i have a test in 20 minutes and his videos saved my life
Thank you sr!
Useful... thank you..
ty
Thank you so much man!!!! You are awesome!
When the pen hovers closely above the tablet, the mouse is responsive. You don't have to be in contact with it. I use one for Photoshop and that's how mine works.
are the vectors associated with each free variable linearly independent always?
Yes because only that vector associated with the free variable has a 1 in it, whereas it is 0 in the other vectors. So these vectors are always linearly independent after rref since theres no linear combination to represent that "1"
i wish i can hug uh for ur help
perfect!!!
God Bless..
Excellent video, though why does the calculation for nullspace start with B but end with A?
Damn this was really helpful.
so good
I cant find this complete playlist? Please link anyone? :,(
Let me ask you a question... is number of non pivot columns the nullity of a matrix and number of pivot columns is the rank of the matrix?
yup
your handwriting is just like mine!
Jeeeez what snoozzzzeefest. #YAAAAWWWWWNNNN
what if the free variable is not linearly independent?
Then how does he move the pointer around without writing?
Sick
It actually doesn't need to be in RREF btw. REF will work better since it's a time saver.
Row eschelon form is good enough because the numbers will change but the pivots will not. Since the rank-nullity theorem is dealing strictly with the # of pivots col and # of non-pivots col
basically the number of free varible in the matrix is the dimension of the null space. Dude why must linear algebra has so many terms. nullity = dimension of null space = numberof free verible in rref. Spend 10 min just want to know this and is at the last part of this video....
Teach at my school please???
how are x2, x4, x5 free variables?
If you look at the columns of the rref matrix, they do not contains any pivot ones. So if you were to expand the rref matrix, the free variables are the ones that appear in both equations.
luv ya m8
thx mate..u saved me from failing maths.....lolz
why is my linear algebra class not using matrices--
God I love you.
I'm pretty sure he uses a USB tablet to do these
I wanna kiss you right on the fuckin mouth Mr. Khan Academy
beast mode!!
Hes so smart, not even funny