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.
Hi all! Wanna help a TH-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
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!!!
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!
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!
If the TH-cam tutorial sucks, no one will watch their videos. More views = more TH-cam 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.
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
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
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!
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
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
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 :)
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.
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?
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?
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!!!
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.
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.
For some reason no other guide could point out that you take the corresponding columns from the original matrix based on the leading zeros in the rref matrix to get the basis. I wonder why it works.
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.
that is weird, one of the requirement to have basis is linear independence. But ,at the beginning, he stated that all vectors had not been linearly independent already. How come it still have basis?
The basis is just the part of the set that is linearly independent. That's why you take only the pivot columns. It has a basis doesn't mean it is a basis.
Yes, there are infinite. No, he could pick every combination of two independent vectors at that paper. Only criteria to answer this question is choosing two independent vectors "in the defined column space".
So yeah, for part (i) you do the row operation for all the vectors U , W and get a general solution. (say its v1) But its (ii) that im confused. What i did was find the general solution for U itself, say the solution are v2,v3. Then the basis for U would be {v1,v2,v3}. How I found the solution for U is, after the row operation, I set x3 =a and x4 = b which gives two solutions, and 3 in total including U intersection W. Similar for finding the basis of W.
There are 2 method to find the basis right? First one is the one he did which is the pivot columns are the column basis and the other method is reduce the matrix until it can no longer be reduced further and the remaining rows are the basis.
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)
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.
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?
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?
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.
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.
However when I checked the answers, they have done it by setting x4 = 0. Which results in total 2 solutions ( 1 from U intesection W and the other from U only) Although the answer notes "many other possible answers", I wonder if the solution I found is valid.
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.
a basis is a spanning list that is also linearly independent. A spanning list, spans a vector space, which you are correct is a subspace of said vector space. A subspace is still a vector space. So a basis therefore also spans a vector space. A vector space is a set of vectors that have vector addition and scalar multiplication. Hence why you can talk about a basis for a set of vectors. I understand your confusion, but I do believe you are wrong.
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?
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
Thoughts: (1) I arrived at this answer by writing the vectors as rows in a matrix. reduce and all rows except x1 and x2 are 0 rows. Thus, I reasoned that x3, x4 and x5 are linearly dependent relative to x1 and x2. this approach makes intuitive sense to me. (2) approach here (vectors in column form) is not as intuitive to me. Why does this work? What do the pivots in x1 and x2 columns mean conceptually that lets us conclude that these two vectors form a basis for the span?
But whats the reason? Why are the basis vectors = the vectors corresponding to leading entries in the REF? Can anyone provide an explanation? Thank you
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!
+Nick Leon less than 10 minutes...just 7 and half minutes
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.
lầy vãi =))
I know it's pretty off topic but does anybody know a good website to watch new series online?
@Alec Kendall i dunno I use Flixportal. just search on google after it:P -holden
You basically summed up my incomprehensible 45 minute lecture .... thank you so much you are a saint T_T
Hi all! Wanna help a TH-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
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!!!
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!
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!
why youtube tutorials seem to be so much better than paid professors?
Because you actually pay attention to these videos and want to learn compared to class lol
@@mandrew4261 Lol that might be true, other people often distract you
If the TH-cam tutorial sucks, no one will watch their videos. More views = more TH-cam 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.
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
For real
This so far has been the most helpful video I have found for anything in Linear Algebra. Thank you, all these years later.
It took 7 mins for you to explain this better than 2 one-hour lectures i had. Thanks!
I have learned more from a 7-minute TH-cam video than in three hours from my incompetent linear algebra professor. Thank you, good sir.
I have followed you for Calculus 3 and now for Linear Algebra! Thank you for your videos!
Thanks a lot. Much better than my Professor could ever explain
Here comes the Grade savior Patrick!!!!!!
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
wow mate. thanks! something that took my lecturer almost 2 hours to get through takes you 7 minutes, and is SO much clearer too!
You are a blessing from heaven
You are a god. This is so simple. I don’t know why professors tend to overcomplicate such basic ideas
you are the best math teacher i have ever come across ,way too much better than my math professor . stay blessed bro
🔥 THANK YOU, YOU JUST SAVED MY ACADEMIC LIFE.
Thankgod for people like patrickJMT, making things understandable that teachers seem to make much harder on purpose.
This made a lot more sense now. BIG THANK YOU!
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
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.
Finally a Basis video that makes sense! Thank you!
TH-cam is an amazing teacher.
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!
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
Thank God for this channel
Bro, you the real MVP. I'm telling ya, you deserve a dragons unlike that unworthy Daenarys. Still not over GOT ending :(
so thorough....thanks god i've found you just before my math225 midterm tomorrow
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
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 :)
Exam tomorrow; I was overwhelmed until I found this video
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.
Conclusion:
after applying rref(matrix)
Basis = linearly independent columns = pivots = dimension of C(A) = rank of aug. matrix
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.
Went back to the beginning and the question I had originally asked as a comment, was answered.
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?
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?
if rank is 2 then you don't need more than two vectors to form the basis.
thanks man!! u explained so simply.... helped me A LOT!
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!!!
If only i found this video earlier, im sure my concept on linear algebra would have been much clearer!
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.
05:53 Thats row echelon form, *not* "reduced" row echelon form, when there are all zeroes above the diagonal
This is amazing! Thank you so much!
so the basis set of vector is same as basis of the column basis ?, how about the basis for row and null space ?
Thank you. Simple and beautiful.
Hey Patrick,
You should put these linear algebra vids into a linear algebra playlist :)
This really helps a lot! Thank you very much!
The 6 wide matrix is when I noped out in class, so now I'm here.
thanks dude, nicely made video
THANK YOU! amazing explanation!
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.
Not everyone on youtube is as good as PatrickJMT though
thanks bro it helped me alot
😄
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
Span = infinity if dependant.
your way of expalaining is very nice .....
You are amazing man ! ☹ thank you a lot
For some reason no other guide could point out that you take the corresponding columns from the original matrix based on the leading zeros in the rref matrix to get the basis. I wonder why it works.
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
Fuck me! It works! You just saved my ass again. Thank you, Patrick.
BreezyMuffins
Bahahahaha! Touché.
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.
that is weird, one of the requirement to have basis is linear independence. But ,at the beginning, he stated that all vectors had not been linearly independent already. How come it still have basis?
The basis is just the part of the set that is linearly independent. That's why you take only the pivot columns. It has a basis doesn't mean it is a basis.
Basis vectors for the 6 that were there are infinite correct? Or must it always use the first column and second column, no right?
Yes, there are infinite. No, he could pick every combination of two independent vectors at that paper. Only criteria to answer this question is choosing two independent vectors "in the defined column space".
omg! thanks!~ this was super helpful!!!
I don't understand, I was taught that this is how you find the basis of the COLUMN SPACE of the vector space...
So yeah, for part (i) you do the row operation for all the vectors U , W and get a general solution. (say its v1)
But its (ii) that im confused.
What i did was find the general solution for U itself, say the solution are v2,v3.
Then the basis for U would be {v1,v2,v3}.
How I found the solution for U is, after the row operation, I set x3 =a and x4 = b which gives two solutions, and 3 in total including U intersection W.
Similar for finding the basis of W.
There are 2 method to find the basis right? First one is the one he did which is the pivot columns are the column basis and the other method is reduce the matrix until it can no longer be reduced further and the remaining rows are the basis.
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)
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.
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?
Super explanation sir thank u
nptel open course from IIT india is really helpful . It has video lectures in your field.
God bless you bro
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?
its great better thn khan acad's counterpart of the same series
+Divyang Vashi go their website and tell them this. everyone knows this except for them.
I agree with you 100%
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.
he might not to the hardest examples but he explains the concepts better than anyone ive found. certainly better than professors
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.
Is it possible to use the determinant off all vectors to see if it even exist a basis for a set of vectors?
can u use gausian to so this
Spectacular 🫡
I have a question here. Is basis for a set of vectors the same as basis null space?
However when I checked the answers, they have done it by setting x4 = 0.
Which results in total 2 solutions ( 1 from U intesection W and the other from U only)
Although the answer notes "many other possible answers", I wonder if the solution I found is valid.
Quick question, is the dimension of the matrix in the example 2?
Cheers
i have a few videos on circuits, but not a ton
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.
I think you mean the basis for the span(S) which is a subspace. One cannot talk about a basis for a set of vectors
a basis is a spanning list that is also linearly independent. A spanning list, spans a vector space, which you are correct is a subspace of said vector space. A subspace is still a vector space. So a basis therefore also spans a vector space. A vector space is a set of vectors that have vector addition and scalar multiplication. Hence why you can talk about a basis for a set of vectors. I understand your confusion, but I do believe you are wrong.
Whats the difference between this and finding a basis for R3, with a given set of vectors?
You're the man !!!!!
absolute legend mate
U are god man
Subscribed
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?
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.
I wish you were my professor in college . Come teach math at Stony brook University.
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
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
But I thought you said the vectors needed to be linearly independent for them to form a basis?
But if you are in R3, shouldn't you have 3 vectors as your base ?
so we take vectors as basis which becomes row echelon or what?
How did you got that those vectors are the basis
If the basis for a solution space is the zero vector, will the dimension for the solution space also be zero?
I don't think so. Zero vector is in all dimensions.
Thoughts: (1) I arrived at this answer by writing the vectors as rows in a matrix. reduce and all rows except x1 and x2 are 0 rows. Thus, I reasoned that x3, x4 and x5 are linearly dependent relative to x1 and x2. this approach makes intuitive sense to me.
(2) approach here (vectors in column form) is not as intuitive to me. Why does this work? What do the pivots in x1 and x2 columns mean conceptually that lets us conclude that these two vectors form a basis for the span?
But whats the reason? Why are the basis vectors = the vectors corresponding to leading entries in the REF? Can anyone provide an explanation? Thank you
Are the first two vectors also linearly independent?
Yes since each of their columns have a "leading 1".
How does the computation explain why the answer is a basis. Like in words why is that the basis
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