Determining whether a transformation is onto | Linear Algebra | Khan Academy
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- เผยแพร่เมื่อ 18 ธ.ค. 2024
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Determining whether a transformation is onto
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You're not overstating anything when you talk about the last row of the augmented matrix not being zero sometimes, for some set of b1, b2, ...bm. You're speaking precisely, and what you're saying isn't self-evident. Very much appreciated.
i learn more from this video than my linear algebra professor....
This was the most helpful TH-cam video I have watched to this day. Thank you so much Sal.
I think this is a great video, very educational.
Thank u sir
Clear explanation
in short, the vector that has been transformed by the matrix function must be a member of the dimension of the vector in the right side of the augmented matrix. in general, in order to deduce that the matrix function does make the transformation surjective. we put it in an augmented matrix with any given vector from R^m then the number of pivot entries must equal m, because m is the number dimensions we ought to transform a vector to. (please correct me for any errors)
Thank you!
nice channel ! What kind of software and hardware do you use for writing ?
Sal, you have 2 basis vectors bit 3 rows?
Ok I think I know where the confusion was for me and someone below, sal has two pivot columns highlighted here, but he clearly has ...... between rows, so he has more than two rows in the matrix shown.
excellent :)
But you clearly don't have a pivot entry in every row in the diagram shown? You have really confused me
This courses are helpful but you are repeating yourself very often and that is extremely annoying.
The captions for this are kind of poor. I offer a hand captioning service, though I'm not sure if you could afford it right now.
Thank you!