Video není dostupné.
Omlouváme se.
Introducing Linear Combinations & Span
Vložit
- čas přidán 14. 08. 2024
- We saw Vector Addition & Scalar Multiplication in 1.3 Part I. Now we take arbitrary combinations of those two arbitrations, called Linear Combinations. We can compute this algebraically and visualize it geometrically. The set of ALL linear combinations is called the span. In some cases this is set is everything, sometimes just a line, sometimes even just the single zero vector! Two vectors are particularly nice, called the standard basis vectors whose span is immediately able to be determined.
Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!
Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
This video is part of a Linear Algebra course taught by Dr. Trefor Bazett at the University of Cincinnati.
BECOME A MEMBER:
►Join: / @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: www.amazon.com...
For anyone wondering how he got those values at 3:07
We know that there is some value of x and y such that:
x(2) + y(-1) = (0)
(1) (1) (-2)
Now this is nothing but
2x-y=0
x+y=-2
(Just did some scalar multiplication)
This is a linear system of equations and now we can continue to find the values of x and y if they exist.
(2 -1 | 0) -----------------> (2 -1 | 0)
(1 1 | -2) R2 -> R1+R2 (3 0 | -2)
Now we can substitute the values.
3x+0y=-2
x=-2/3
2x-y=0
2x=y
2(-2/3)=y
-4/3=y
And we're done!
Sir every maths students need the teacher like you . You made my day love you sir. Love from india
This is a great series! There are many concepts I found hard to understand when I took this course. You've made them clearly understandable!
The whole idea of lineae combination is explained in one minute. I always come back to this video whenever i lose the concept of what is actually a linear combination.
Thank you so much for dumbing down the concept to us mortals.
A few months ago I commented on your video; why your channel has mere 69k subscribers, coz u deserve a lot more... And now I see 112K... I knew it. Good things take time to be successful, and now I see a positive sign.
Thanks a lot for making the math so beautiful.
Thank you so much 😀
and now 317, amazing
Daaaammmn, I didn't understand this at the uni lecture, and now I understand from your video!!
this video is really helpfuul for me thnk uh sir respect from india
Thankyou for thanking a person for entire india you made my work easy . Now I don't need to thank him.
This compilation is juts t beautiful, I don't know how to thank you
Absolutely outstanding videos!
Thanks again & again
I loved the explanations. No wonder if u get 1 million subscribers.
I hope so!
Love your course. Legends like you saves us all.
Thanks for the beautiful lecture. Back to basics.
Thanks from Republic of Korea~^^
You are cxcellent !!!!! You have no more subscriber but i will suggest this chennel of my math friend. Love from bangladesh.
Thanks from Uzbekistan
These vids are perfect and admirable.
Too good sir
My thanks are basis vectors and I give the span of them to you.
Awesome videos. Definitely a good LA refresher
Concise and clear. Thank you
Awesome expanations, thanks!
Appreciate the effort 👍
Thank you so much sir!
Very nice, please make a video on an affine combination, a conical combination, and a convex combination.
Thank you :))
thank you sir
🔥🔥🔥
Never stop making videos.
great vid, thanks :)
Hi,
If Cartesian Coordinate System gives just scalar multiplication to basis vector (i, j).
What are polar coordinates doing... In which one in just scalar distance(r) and the other angle is?..
Which type of tensor is angle in the set of (distance, angle, area volume).
Could you make sense of this....
Thank you sir , your videos are very helpful :)
Can you suggest me any reference book for algebra
In one of the comments for the 7th video in this playlist, Trefor recommends the free and open source textbook joshua.smcvt.edu/linearalgebra/#current_version 🙂
@@BiancaAguglia Thank you 😁
thanks a lot sir. also thanks miss ism who shared this video :)
Informative series Dr. Trefor. Though, you are using too much energy to illustrate without the need to do so. Try to reduce the amount of energy you are using to explain things. It will be beneficial for you & us.
thanks doc ur a g
04:32 get to the Point :D thanks from germany
Amazing lecture! I have a question ! If I have span of two vectors and I have a vector indepedent from the span of the two vectors. Does it look still as a plane ? If yes, is the plan finite or infinite ?
no, if you have two vectors and a vector independent from the span of the two vectors ,then the set of the two things doesn’t lie in a plane .instead they will lie in a 3D space
Hey Trefor,
Sorry for the silly question but i got a doubt about the the minimum dimension a vector could exist.
You've said in the video that Xi belong to R and vectors (ai) belong to Rm.
And in your previous videos you started talking about vectors using a plan, which is R2.
So my question is can i have a vector in R ? If yes or no please tell me why.
Kind regards
Hey Trefor,
What you've said helped me a lot, and it makes more sense to me know cause if the vectors are in R^n and n > 0 then R^1 is part of R^n. So it's clear for me now. But i would like you to explain what you meant by saying "When we use R^1 we are thinking of it as a vector space in its own right." please.
Thank you very very very much for helping me
@@daoudatraore930 R is the set of real numbers - you can multiply any n-dimentional vector from Rn with a real number.
On the other hand, if you're looking at a line - R1, that is, a one-dimentional vector space, and have fixed a center O, then the vector space R1 consist of single-dimentional vectors, represented with a single number from R, but nevertheless we still think of them as vectors.
I think your confusion stems from the fact that we're looking at a single object from two different points of view - once, R is the set of real numbers, and then - a 1D vector space. (1)
By the same logic though you can be confused about R^n being the set of ordered n-touples of numbers like (1,...,n), and at the same time - a vector space of n-dimentional vectors. (2)
The relation in (1) and (2) is the same - but yet, you're not confused by the latter. Try to see how (1) is the same as (2), accept it and let your confusion vanish.
You might want to use stronger, brighter neon font colours against gray/dark backgrounds, as there are some colour-blind viewers. And also night blind viewers.
Your red fonts and blue fonts are indistinguishable to my eyes, their hues lost in gray background. Opt for neon colours, that are brighter and more distinguishable.
Very informative video, but the audio quality is a little bit distracting
Crybaby
@@gordongoodwin6279 lmao who hurt you?
@@bas73971 my family was very abusive and it made me an ahole
@@gordongoodwin6279 😄
i think this video could have been more simple
Dark blue is not a good color