Let T:V→W be a linear transformation where V is an infinite-dimensional vector space and W is a finite-dimensional vector space. What is the dimension of the kernel?
Hello everyone. Sorry my English, it's not my first language.
I tried doing this:
But V has infinite vectors, so remaining vectors are in the kernel.
I don't know if I can use dim V = dim KerT + dim ImT here.
I'm not sure of the things I said. If someone may help me I would appreciate a lot. Thank you very much for attention!