Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy

Example involving the preimage of a set under a transformation. Definition of kernel of a transformation.
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[@Powd3r81]

I can't tell if this video is a good one or not. Linear Algebra just became so freaking hard and none of the math makes any sense. All these vector spaces and sub spaces are so abstract ughhhhh

[@spag5296]

7 years later, I'm feeling the same way! although the video was explained much better than my lecturer.

[@aminem4626]

I feel you haha

[@razberrycreme]

How are you such an amazing teacher, seriously. It would also be really helpful if you numbered your videos so that we know what order to watch it in. but seriously these are amazing. thank you!!!!!

[@thomasvitale5250]

At 0:13 when he coins the term "multiplation" :) Muchas gracias Khan Academy brothas! Your videos are helping me through grad school! Who needs professors on tenure anyways :)

[@Bomberofdoom]

SO THAT IS THE NULL SPACE!!!!! :-O Why couldn't they explain this at the same time they explained us about the null space?!?!?! Now that I VISUALLY see it, I can really understand what we're talking about! Thanks Sal!!

[@Sheeeeshack]

Little hair splitting: Kernel is a kind of transformation. It’s not all the vectors. That is basically the difference with NULL.

[@grandorottcod1]

kernel== nullspace

[@linkwigger]

Great explanation of the nullspace of T.

[@debendragurung3033]

13:16 bookmark, a set of vectors in one domain gets mapped to just a single set in range. Yet still a linear trasforation..... neat

[@Waranle]

Thank you Sal

[@farmerdave4000]

Thanks for the explanations!

[@Zmunk19]

does this have anything to do with the kernel trick in support vector machines? (machine learning)

[@ad2181]

thank you

[@xybersurfer]

good explanation

[@abhishekagrahari1007]

great explanation

[@gubby740]

thx

[@s0m0c]

Gracias!

[@mappingtheshit]

Well, I study physics, and for me it is more natural that kernel is the mapping into the identity elements... Or is it just in pure mathematics kernel is mapping to any desired elements?

[@DJDKCR]

I like to skip ahead and watch these advanced videos so that I can see what I will be able to understand someday.

[@haythemoldaccount7953]

I am doing this freshman year help

[@rainerrustenberg3824]

I just wonder, that if you will combain the equations at time 7:45 it wil be a contradiction. Why, because: x1 = -3t and, ( x1 - 1 = 3t, gives x1 = 3t + 1), so ( x1 = -3t AND x1 = 3t = 1), but that is when solving 2 linear equations with 2 unknown, sorry, I'am bad. But it sure is a great video, very well. Rainer

[@floyd617]

i thought it would be shifted one up, how is it to the right?

[@spaceteapot]

does he mean the space spanned by the vectors S? because S itself is not a subspace.

[@mappingtheshit]

@mappingtheshit or am I just confusing the simple matrices with groups?

[@devilpizza123]

lol multiplation :D