Finding Basis of Kernel and Range of a Linear Transformation - Linear Algebra

What is a Kernel and Range of a linear transformation? How do we compute these and find their respective basis? This video aims to answer these questions.

[@ctamai]

This video is by far the most thorough and best explanation. I love that Drew does a short review before solving the problem. He makes it so easy to understand the concept.

[@DrewWerbowski]

Thank you so much for the kind words!

[@JackH.122]

Very nice, thanks. Didn’t really get it in class and in the book, but now I understand.

[@DrewWerbowski]

Glad it was helpful! Thanks for leaving a comment!

[@Shsnaiaahnahia]

my fav content creator drew werbowski

[@wither8542]

thank you so much for making this video! :) I was wondering if you could possibly explain one-to-one and onto?

[@yaminisharma7676]

Thanks a lot, from India

[@islamicprincess4820]

i have a question
here basis of kernal is empty then.it has no dimension..means zero dimension.but dimension.of Kernal equals nulity so here we seee nulity is 1

[@GOKU_BLACK_100]

AWESOME EXPLANATION 🌟

[@user-kx8du3js7f]

Great video! Thanks

[@islamicprincess4820]

So why nulity is 1?

[@bethusilegamedze946]

Please help, i still don't get how you got the kernel to be zero.

[@DrewWerbowski]

Our matrix only has the trivial solution (x1=x2=0). If this isn’t clear then review how to read solutions from a matrix

[@KaterinaKozmin]

what is there is a free variable in the reduced form?

[@Jaylan...]

For the Kernal you set the free variables of rref equal to t, s, r... , solve for each vector in terms of these, giving the span of the nul space aka kernal. For the Range you'd use the rref pivots/leading 1's , use only the corresponding columns from the original matrix, that should be your answer.
Cool vid btw :)

[@jeevans7656]

nice video

[@teslayt940]

👍

[@Shsnaiaahnahia]

next upload when

[@GeorgeHuang-ws2rf]

drew im michael from f8f pls respond

[@starmist1691]

Bro left us and now we're stuck with mrs frost again-
(Also the only other person in the comments ik is Michael- im suprised i havent seen anyone else ik)
How many eggs could fit into a microwave 👨‍🦲