Column space of a matrix | Vectors and spaces | Linear Algebra | Khan Academy

Introduction to the column space of a matrix

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[veryweirdoccurance]

12 years later and these videos are still relevant. Khan was a visionary. Thank you so much for your work, you pioneered modern education

[manigawari]

It will be more convenient if you number the videos, so that we'll know which to learn first

[djprometheus]

people coming on here saying it wasn't helpful probably haven't started the linear algebra series from the top. this video is great

[Mobboss]

I don't know if you are aware of this Sal, but you reign on the bad-ass supreme in the department of tutorial videos. If I ever can't explain something to a friend I refer them to your site with "Sal will explain it to you." - True support!

[ozzyfromspace]

This was implied, but I just wanted to state it anyway: given a simple equation like Ax=b, before solving the equation, you might wanna first check to see if b is a member of the column space of A. If it is, then you can expend energy trying to calculate x. If not, you shouldn't waste your time because no solution exists. When your doing more complex things, this could save you a lot of time because you know which computations will fail ahead of time. Very interesting!

[davidkim]

is everyone just mindlessly saying thanks sal? or did you guys genuinely learn something about column spaces here..? cuz i have no idea what sal was talking about and i need to know how to determine the column space of a certain 3x3 matrix.

[rock.climbing.stuff]

Love this. Linear Algebra test tomorrow covering everything from Null/Column Spaces to linear Transformations, Basis, and Eigenvalues. This is so helpful. Thanks again.

[tornado]

i'm having trouble distinguishing between the basis for the column space of H and the basis of the entire set of H. The basis is a set of linearly independent vectors that span H, but isn't that technically what the basis for the column space is as well?

[jackandaddie]

It makes me sad to see videos like this with few comments but high views. It's obvious this video has helped far more then is obvious by looking at the comments.

I will definitely step up and take 10 seconds out of my homework time to say thanks very much for posting videos like this, it helped me a lot and I will be returning to watch more of your videos.

[Elpresidentification]

Someone please correct me if I'm wrong, but I think that you get the echelon form of the matrix, see which columns have pivots, and then the column space is the set of those columns in the original matrix. So if the reduced form has pivots in columns 1, 2, then the column space is columns 1, 2 in the original matrix.

[morgantaylor]

If matrix A (nxn) is a nonsingular matrix, what does that say about the column space of A?

[ABlindMoose]

A great video! The same rules apply for row spaces (except its span{row vectors} instead of span{column vectors}) right?

[imbsalstha]

your lecture r so effective than a course book.thanks a lot.

[NotmyYTchannel]

Thank you!! I was working on this topic for coming up Midterm

[TVH_life]

Sir I have a doubt about ques related to column matrix can you please help me in this

[grandorottcod]

so column space is basically a representation  of the set of all subspaces of Rn

[umbralTorturer]

Can the "vector" x be a n by p matrix. That is, is this argument still satisfied if x is a matrix and not a vector?

[Pixel]

4:37 for { Ax | x as a member of R^n }

[MellowMuch]

i am very very much confused by this because in my book it specifically says that the rowspace is a subspace of R^n, NOT R^m, and the column space is the subspace of R^m. Is this a typo?

[guicapone]

is this the same as rank of a matrix