[Linear Algebra] Span of Vectors

We talk abou the span of a set of vectors in linear algebra.

#LinearAlgebra #Algebra #UniversityMath #Lecture

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We introduce the notion of vector span, which is the set of all possible linear combinations.

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[adeelali]

I'm studying Undergrad math (Linear Algebra) and this is clearing up a lot of things! Thank you :)
I hope you have a vector calculus playlist :D

[thmtrngh]

i am not a native English speaker and i am studying math in English. but i cannot understand my teacher weird ass English and her ways of giving lecture and you really enlightened me thank you

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[sondernfy]

This was awesome!
I have a Linear Algebra test in four days and your videos are a lifesaver.

[bruceedward]

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[christinedeng]

you're a legend thank you for helping me pass my linear algebra course. much love

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[kharaks]

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[cusipadilla]

really great video, this helped me out so much! thank you!!

[trillonairesclub]

trust me you aee so good at ĺinear algebra awesome God bless you

[tamarshai]

I have similar question and after doing the steps as you did, I got a free variable, what does that mean? that there is infinite many linear transformations thus vector b is in the span?
or did I get it wrong?

[valentinadandan]

hello, is the span considered a region in which the vectors are included in?

[RobsoonQ]

Your vids are really good. Keep up with good work.

[uzairahmadkhan]

Hello, very helpful video, the span of two vectors is a plane. what will be the span of three vectors( will it be volume)? and what will be span of higher combination like four vectors and five vectors??

[XXgamemaster]

I've always wondered, why use a matrix when we could just write down the system of linear equations and then solve for the coefficients x_1, x_2, and x_3 as you did at 6:05? Wouldn't it be more efficient to just write down the equations right away instead of using a row reduction method?

[MM-vwck]

I have 5 days to learn all this to help a friend pass linear algebra.

[zainmaaz]

love you, better than my dumb professor

[dominiorrr]

I don't understand one thing. If a span covers the whole plane, meaning it covers R³ in 4:27, shouldn't the vector b automatically be in the span? My understanding is that in this case it simply doesn't cover the whole plane, but why not? I just don't see it.