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Procedure to Find a Basis for a Set of Vectors 

patrickJMT
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Procedure to Find a Basis for a Set of Vectors. In this video, I start with a set of vectors in R_3 and find a basis for those vectors. The basis is NOT necessarily unique!

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11 сен 2011

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Комментарии : 209   
@shooter16101
@shooter16101 9 лет назад
I wish you could be my linear algebra professor. I learned in 10 minutes what it took my teacher 2 hours to badly explain. Thank you!
@Dotrade
@Dotrade 8 лет назад
+Nick Leon less than 10 minutes...just 7 and half minutes
@Forgetit2697
@Forgetit2697 7 лет назад
He said "I learned in 10 minutes". No where in his sentence did he specify that it took him ten minutes to watch the video, or the length of the video for that matter. He simply stated "I learned", therefor, he may have watched the 7 and a half minute video and paused it to think etc.
@phuccoiinkorea3341
@phuccoiinkorea3341 6 лет назад
lầy vãi =))
@aleckendall5101
@aleckendall5101 2 года назад
I know it's pretty off topic but does anybody know a good website to watch new series online?
@holdenmilo24
@holdenmilo24 2 года назад
@Alec Kendall i dunno I use Flixportal. just search on google after it:P -holden
@SpektreProxy
@SpektreProxy 9 лет назад
You basically summed up my incomprehensible 45 minute lecture .... thank you so much you are a saint T_T
@yalinlu8564
@yalinlu8564 7 лет назад
why youtube tutorials seem to be so much better than paid professors?
@mandrew4261
@mandrew4261 5 лет назад
Because you actually pay attention to these videos and want to learn compared to class lol
@That_One_Guy...
@That_One_Guy... 5 лет назад
@@mandrew4261 Lol that might be true, other people often distract you
@Nicksperiments
@Nicksperiments 4 года назад
If the RU-vid tutorial sucks, no one will watch their videos. More views = more RU-vid ad revenue. Professors get paid the same regardless of the quality of teaching so they have no incentive to do good. Also like The Duke said, professors do research too which is really what gets them the money.
@jenna_maria
@jenna_maria 4 года назад
Also youtube tutorials may appear easier because you've already been introduced to the complicated stuff in class, so watching slightly easier stuff a couple more times after that seems a lot easier. Nonetheless, this guy did a great job explaining the topic
@to.the.tech.world.official
@to.the.tech.world.official Год назад
For real
@josphine291
@josphine291 8 лет назад
Patrick MAN you always save my life. You saved my life in my calculus class. Now you are here saving my life in my algebra math class. I told all my friends about you and they love you so much! instantly subscribed!! Please upload more of these + if you can upload some STAT math videos that would be awesome!!!
@TheARizzle101
@TheARizzle101 11 лет назад
I have learned more from a 7-minute RU-vid video than in three hours from my incompetent linear algebra professor. Thank you, good sir.
@jakedornhecker1202
@jakedornhecker1202 11 лет назад
I've been watching your videos since I came to college because you are far more helpful than professors. I wish you had more videos for linear algebra, but you really saved me with this one. Thanks for all the videos you've made!
@jenniferf6265
@jenniferf6265 8 лет назад
I love, love, love ALL of your videos. I wish you were my Professor. My professor sounds like a walking textbook. You definitely dumb things down and make it much easier to comprehend. Thank you for the great videos!
@whatthego
@whatthego 9 лет назад
Here comes the Grade savior Patrick!!!!!!
@ninefoldrin5507
@ninefoldrin5507 2 года назад
This so far has been the most helpful video I have found for anything in Linear Algebra. Thank you, all these years later.
@Crestedsquash
@Crestedsquash 10 лет назад
Thanks a lot. Much better than my Professor could ever explain
@anna230999
@anna230999 6 лет назад
Thank you so much for these videos, you have single handedly saved my Linear Algebra grade. You explain everything so well and at the perfect pace
@hbari591
@hbari591 9 лет назад
I have followed you for Calculus 3 and now for Linear Algebra! Thank you for your videos!
@TheKSRBroadcast2Home
@TheKSRBroadcast2Home 4 года назад
Why do profs even bother with all the technical terms, just explain how to do and use the terminology as it's taught. Thank you for your tutorial, as others have said, your video was incredibly clear and concise. I very much appreciated the fact that it was this way
@SomethingSoOriginal
@SomethingSoOriginal 12 лет назад
It took 7 mins for you to explain this better than 2 one-hour lectures i had. Thanks!
@afsarabenazir8558
@afsarabenazir8558 6 лет назад
Your videos are amazingg! so much clarification and man, i feel so grateful to you for making these videos. Don't know if i would pass in my math course without these
@icecoldpierre
@icecoldpierre 7 лет назад
Finally a Basis video that makes sense! Thank you!
@clprinceton
@clprinceton 9 лет назад
You are a blessing from heaven
@thomaslange6065
@thomaslange6065 6 лет назад
Dear Patrick, please provide a video covering the four fundamental subspaces (the left null space in particular?). No one can do this wonderful piece of art like you can!
@masonralls1980
@masonralls1980 3 месяца назад
You are a god. This is so simple. I don’t know why professors tend to overcomplicate such basic ideas
@tkhampa
@tkhampa 9 лет назад
you are the best math teacher i have ever come across ,way too much better than my math professor . stay blessed bro
@autogordel
@autogordel 12 лет назад
Thankgod for people like patrickJMT, making things understandable that teachers seem to make much harder on purpose.
@sn0wchyld
@sn0wchyld 12 лет назад
wow mate. thanks! something that took my lecturer almost 2 hours to get through takes you 7 minutes, and is SO much clearer too!
@lamtartarus
@lamtartarus 12 лет назад
you, sir, are a life saver. thank you for these videos. now i dont have to spent money to attend extra seminars for the upcoming midterm.
@darkdamian938
@darkdamian938 2 месяца назад
🔥 THANK YOU, YOU JUST SAVED MY ACADEMIC LIFE.
@brandonfigueroa2800
@brandonfigueroa2800 2 года назад
This made a lot more sense now. BIG THANK YOU!
@matejbeno569
@matejbeno569 6 лет назад
Thank you very much for the explanation, I also have a question, is that also a basis of vector space ℝ^5? Or only the set of vectors that form the linear span?
@rusafmomen2718
@rusafmomen2718 11 лет назад
thanks man!! u explained so simply.... helped me A LOT!
@IsaacSung
@IsaacSung 12 лет назад
RU-vid is an amazing teacher.
@ralchemist1122
@ralchemist1122 11 лет назад
dude I don't know what you do for a living but you'd rock at being a teacher!!! thanks man! my exam's tomorrow and this helped out a lot! =] wish I had found this earlier
@Mary-gr3mr
@Mary-gr3mr 6 лет назад
Exam tomorrow; I was overwhelmed until I found this video
@SuperSmitty9999
@SuperSmitty9999 6 лет назад
It would be awesome if you could do an example of finding a basis for R3! Still you did a great job of addressing how it would work, you would have three rows with leading ones, well said thank you!!!
@siyihuang3532
@siyihuang3532 10 лет назад
This really helps a lot! Thank you very much!
@SymphOcta
@SymphOcta 6 лет назад
THANK YOU! amazing explanation!
@alexiadrey938
@alexiadrey938 3 года назад
Thank you. Simple and beautiful.
@lamnguyentunglam585
@lamnguyentunglam585 5 лет назад
so the basis set of vector is same as basis of the column basis ?, how about the basis for row and null space ?
@vincelunceford
@vincelunceford 11 лет назад
so thorough....thanks god i've found you just before my math225 midterm tomorrow
@andyhype2546
@andyhype2546 4 года назад
Bro, you the real MVP. I'm telling ya, you deserve a dragons unlike that unworthy Daenarys. Still not over GOT ending :(
@andrewdeuriarte9147
@andrewdeuriarte9147 7 лет назад
At 6:45 you said that if the fourth column had a nonzero element you would need to use those four vectors, but you only moved your finger on three columns (vectors). So do you use the column in between, or do you only use the three vectors?
@yazy91
@yazy91 12 лет назад
omg! thanks!~ this was super helpful!!!
@sarag.regassa7947
@sarag.regassa7947 Год назад
This is amazing! Thank you so much!
@fatimaaftab9378
@fatimaaftab9378 Год назад
Thank God for this channel
@skyphio6266
@skyphio6266 8 лет назад
Went back to the beginning and the question I had originally asked as a comment, was answered.
@josephbensen5363
@josephbensen5363 5 лет назад
You are the man!
@mesmeriz3
@mesmeriz3 12 лет назад
If only i found this video earlier, im sure my concept on linear algebra would have been much clearer!
@sameerthor11
@sameerthor11 Год назад
thanks bro it helped me alot 😄
@keidaniel8494
@keidaniel8494 8 лет назад
thanks dude, nicely made video
@halaabubaker3899
@halaabubaker3899 5 лет назад
You are amazing man ! ☹ thank you a lot
@ArjavPatelpatelarjav15
@ArjavPatelpatelarjav15 9 лет назад
Thanks man !!!
@badman477
@badman477 7 лет назад
God bless you bro
@rajeshkannan2903
@rajeshkannan2903 3 года назад
Super explanation sir thank u
@pancakes465
@pancakes465 10 лет назад
Hey Patrick, You should put these linear algebra vids into a linear algebra playlist :)
@JoshPity
@JoshPity 13 лет назад
My algebra professor called that gausjordan or something crazy, where were you when I was doing this last year! At least I found you for my applied calc class haha! Keep on going on.
@Thadnill
@Thadnill 6 лет назад
Is it possible to use the determinant off all vectors to see if it even exist a basis for a set of vectors?
@bijoudeaux1
@bijoudeaux1 10 лет назад
Hi. I watched this video and the one before, but I am confused. Our lecturer stated that we should form the matrix from the set of vectors given by writing each column vector as a row vector. Afterwards, EROs are used. I don't understand this technique and how it relates to the one you are using. Your method seems easier but it is difficult to grasp right now seeing that you did not write the column vectors as row vectors...Is there a reason why you did not write it that way? Thanks.
@HarryX10
@HarryX10 10 лет назад
Thanks a lot. very clear.
@mariaangelasanpedro9892
@mariaangelasanpedro9892 7 лет назад
Good day sir :) I just noticed something in 4:51, was it -2R2 -> R3 -> R3 ?? or...-2R2 + R3 -> R3?? But you said " add that to R3", just some little concerns, thank you :)
@HemantSingh-gg5kd
@HemantSingh-gg5kd 6 лет назад
your way of expalaining is very nice .....
@anastasiiamalyk1706
@anastasiiamalyk1706 4 года назад
Correct me if I'm wrong, but for a basis in R3 we need three linearly independent vectors, but in our case we found only 2. 2 vectors do not span R3 and thus, they cannot be called a basis?
@Richa_cute
@Richa_cute Год назад
if rank is 2 then you don't need more than two vectors to form the basis.
@lukelam8366
@lukelam8366 8 лет назад
Great video, thanks! At 6:40, you said if 4th column turns out to be a 1, you take the 4th column. What if it isn't a 1, but a+1? Thanks
@GoatMen
@GoatMen 5 лет назад
Span = infinity if dependant.
@jasomraz97
@jasomraz97 7 лет назад
I have a question here. Is basis for a set of vectors the same as basis null space?
@milesistheman
@milesistheman 9 лет назад
This works for row reducing by hand, but say I have to row reduce using a computer, and I have no way of knowing if there were any row swaps performed. How do I know which vectors form the basis in that case?
@abdulrahmankhalifa5284
@abdulrahmankhalifa5284 8 месяцев назад
Spectacular 🫡
@robertbosch99
@robertbosch99 5 лет назад
I have an exercise which I need to solve for homework, I have a matrix A and a transformation T(x) and I need to define x so that A(x) = T(x) Is the procedure for solving this exercise similar to this method?
@missangelinaadams
@missangelinaadams 10 лет назад
Fuck me! It works! You just saved my ass again. Thank you, Patrick.
@missangelinaadams
@missangelinaadams 10 лет назад
BreezyMuffins Bahahahaha! Touché.
@Schoko4craft
@Schoko4craft 6 лет назад
I thought basis are vektors with that you can build any other vektor. Therefore you allways need as many vektors as basis as you have dimensions. That means in this case 3 Vektors but you only have 2. Is this basis another thing or where am i wrong? (I need to get basis of 4 dimensional vektors)
@Knights2theEnd
@Knights2theEnd 6 лет назад
This video is completely wrong. Don't follow it. You have to parametrize each column that does not have a leading 1. Then you separate the parametrized variables to get the basis.
@victor1994
@victor1994 10 лет назад
Quick question, is the dimension of the matrix in the example 2? Cheers
@hexadcml
@hexadcml 3 года назад
wow is it that fucking simple? jeez i have been reading the textbook and the lecture notes but 7 minutes of this video did it. damn
@larrylentini5688
@larrylentini5688 6 лет назад
The 6 wide matrix is when I noped out in class, so now I'm here.
@skdbstjddlek
@skdbstjddlek 13 лет назад
Also, I understood the dimension of a vector space as the number of vectors in the basis. So if a basis be {v1,v2, ... ,vn} for a typical vector space, then its dimension would be n. In this case, if I get total 3 basis for each U and W with one of them the same, then the size of the basis for U + W would be 5. ({v1,v2,v3,v4,v5}) So the dimension of U + W would be 5? or does it not matter since the spanning sets are all 4 dimensioned.
@dijahmasnawi6627
@dijahmasnawi6627 5 лет назад
is it basis bcs there is only a 1 in that column and the other are zeros in that column? help me pls i cant catch up u. thanks in advance
@narrabhavesh9149
@narrabhavesh9149 8 лет назад
how do u find the basis if a subspace has only 2 vectors on R4. say {[3,0,0,1],[0,0,1,1]} are the vectors what is the basis and dimension.
@egehanyildiz
@egehanyildiz 4 месяца назад
GAAAAAAH DAMNNNN helped me alot
@jonathanbeattie129
@jonathanbeattie129 9 лет назад
I can't seem to reason through this and I can't find a solution to this problem online so it must be pretty simple and I just don't get it. How do you find a vector to add to a set of vectors to make a basis.
@laurensgoyvaerts8480
@laurensgoyvaerts8480 7 лет назад
Whats the difference between this and finding a basis for R3, with a given set of vectors?
@alfadelTaqi
@alfadelTaqi 12 лет назад
thank you so much
@-LSC
@-LSC 3 года назад
Conclusion: after applying rref(matrix) Basis = linearly independent columns = pivots = dimension of C(A) = rank of aug. matrix
@ryanjackson0x
@ryanjackson0x 2 года назад
rref helps you find which columns they are, but the values of those columns in rref do not serve as a basis for the original matrix.
@shahwarmukhtar6780
@shahwarmukhtar6780 2 года назад
Tell me how to form 2 different basis. Because the standarad basis we add to vector to make a matrix is same ... then how will we get another different basis
@tudr46
@tudr46 7 лет назад
Thank you.
@Isaacnyakunzujr
@Isaacnyakunzujr 10 лет назад
can u use gausian to so this
@TrueTwinify
@TrueTwinify 10 лет назад
Hey Patrick, can you help me do this?? how do I express a 2x1 vector in terms of 2 "2x1" basis???
@yagzyalcntas553
@yagzyalcntas553 8 лет назад
so we take vectors as basis which becomes row echelon or what?
@kelvinthehuman
@kelvinthehuman 4 года назад
amazing!!
@Syedasilalinaqvi
@Syedasilalinaqvi 12 лет назад
Thank you
@rikinshah5367
@rikinshah5367 7 лет назад
I wish you were my professor in college . Come teach math at Stony brook University.
@coffeeblack0
@coffeeblack0 12 лет назад
Not everyone on youtube is as good as PatrickJMT though
@djigi2002
@djigi2002 6 лет назад
U are god man Subscribed
@GSPV33
@GSPV33 6 лет назад
I don't understand, I was taught that this is how you find the basis of the COLUMN SPACE of the vector space...
@sweeseen9577
@sweeseen9577 8 лет назад
great u just tell me the summary for the whole sub topic ☺
@alhaithamaljabri2203
@alhaithamaljabri2203 6 лет назад
My man!
@TKJ0KER
@TKJ0KER 10 лет назад
Are the first two vectors also linearly independent?
@hbari591
@hbari591 9 лет назад
Yes since each of their columns have a "leading 1".
@owenmeeker1663
@owenmeeker1663 3 года назад
thank you
@patrickjmt
@patrickjmt 11 лет назад
i have a few videos on circuits, but not a ton
@prudhvirajsatyavarapu5801
@prudhvirajsatyavarapu5801 7 месяцев назад
How did you got that those vectors are the basis
@Wolverine1o1
@Wolverine1o1 11 лет назад
nptel open course from IIT india is really helpful . It has video lectures in your field.
@whitesanity4965
@whitesanity4965 4 года назад
luv ya keep going m8
@prietoangulocristina6014
@prietoangulocristina6014 5 лет назад
you are amazing
@skdbstjddlek
@skdbstjddlek 13 лет назад
Im studying basis for myself, but having a hard time on one question. The question is: Let U and W be the following subsets of R4( 4th dimension of real numbers) U = {x1+x2+x4 = -x1+x2+x3 = 0}, W = {2x1+x3-x4 = -x1+2x2+x3+x4 = 0} (i) Find the basis of U intersection W. (ii) Find the basis of U and a basis of W, both containing your basis of U intersection w. (iii) Find the basis of U + W containing your basis of U intersection W.
@TheDivyang7
@TheDivyang7 8 лет назад
its great better thn khan acad's counterpart of the same series
@patrickjmt
@patrickjmt 8 лет назад
+Divyang Vashi go their website and tell them this. everyone knows this except for them.
@aaeshaalhebsi1337
@aaeshaalhebsi1337 7 лет назад
I agree with you 100%
@BlackOps78321
@BlackOps78321 7 лет назад
Well, this guy gets too much credit to solve extremely easy problems. You won't always get an easy pre-made example problem where two rows completely cancel out. He only does like the easiest examples of things possible. As a college student who has come here once or twice throughout the years, it has never really helped even if it seems nice because he does the easiest possible example. He also didn't answer the question, he just half-stated the final part of the problem which is never going to be just displaying the 2 pre-given vectors.
@coldhunter7
@coldhunter7 7 лет назад
he might not to the hardest examples but he explains the concepts better than anyone ive found. certainly better than professors
@BlackOps78321
@BlackOps78321 7 лет назад
Hunter Beauclair Of course, because the problem is easy. Some 'professors' are bad but it's true that almost every explained concept here won't help you if you're actually trying to learn it. You're only giving yourself the illusion that you can do it by following a pre-determined easy problem that an 8th grader can solve if given the methodology to do so. These videos tend to give no understanding whatsoever behind more advanced concepts. Generally any academic work would involve almost every other question switching to a new concept, so you might now know how to do #1 but not #2 through #30, and not the next section because you only memorized basic functions. Then psychologically because you procrastinate, as some people do, it becomes the professor's fault when you take the test and don't know how to even begin. Granted, I have had professors that were pretty annoying, but generally people who just aren't smart blame others for their insecurities.
@94suheyla
@94suheyla 11 лет назад
I luv u Patrick :D
@germanamerican81
@germanamerican81 11 лет назад
is this video on the list on patrickjmtDOTcom? cant find it...
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