Oxford Linear Algebra: Rank Nullity Theorem

Links to the other videos mentioned:

As with all modules on ProPrep, each set of videos contains lectures, worked examples and full solutions to all exercises.

The video begins with the definition of the kernel and image of a linear transformation, as well as their dimensions as the nullity and rank of the linear map. Next is a fully worked example of a map in R^2 with an explicit calculation of the kernel, image, nullity and rank.

In the second part of the video the Rank Nullity Theorem is presented: the dimension of the starting vector space of a linear map is equal to the rank of the linear map (dimension of its image) plus the nullity of the map (dimension of its kernel). A full step-by-step proof is then presented by constructing a basis for each component.

Watch the other videos from the Oxford Linear Algebra series at the links below.

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[sebastian]

he doesn't look like a guy who would do maths, but he is a really nice and smart guy

[yanbopan]

The best rank nullity theorem video I have ever seen ;)

[primefactor]

Sir .. please make a lecture on how to extend a basis to another basis ...

[peregrinef]

Did you test 10 to see if 11 was, indeed, the minimum number needed?

[ProGamer-rugd]

you should make a video about jee advance soon

[baltzarbrat]

Sir can you solve
Jee advanced maths question paper ?

[MariadeLourdesAniesSanch-zehf]

I think finish
but my color is pink
because is He

[Hydrogn_]

I thought I could learn something but I'm too young to understand this :Σ

[alphaa]

I'm on that side of YouTube again