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.
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 :)
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
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.
Thank you so much for the kind words!
Very nice, thanks. Didn’t really get it in class and in the book, but now I understand.
Glad it was helpful! Thanks for leaving a comment!
my fav content creator drew werbowski
AWESOME EXPLANATION 🌟
Great video! Thanks
what is there is a free variable in the reduced form?
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 :)
Hey, is the range of a linear transformation the same as find the image of linear transformation?
Yeah
thank you so much for making this video! :) I was wondering if you could possibly explain one-to-one and onto?
Thanks a lot, from India
you should do videos on a black page with white text. Kinda kills the eyes. Great content in the video much appreciated
I appreciate the feedback! Will definitely consider that for future videos.
Please help, i still don't get how you got the kernel to be zero.
Our matrix only has the trivial solution (x1=x2=0). If this isn’t clear then review how to read solutions from a matrix
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
yes
So why nulity is 1?
next upload when
So, the dim(Range(T))=2, dim(ker(T))=0
nice video
👍
drew im michael from f8f pls respond