Hi, I'm having trouble with a couple of questions.
The quesiton reads
A linear operator T on R^4 has the matrix
A= [some 4x4 matrix]
with respect to bases Alpha=Beta=E4.
Find the basis for T(R^4).
-I understand what to do when the question reads find T(1,2,-4,0) or something like that, I'm not sure what to do when it asks me to find a basis for all of R^4.
If someone could please explain the steps on how to tackle this problem I would be appreciative of that.
Secondly, the question later reads
Find the basis of the kernel of T
Find the standard basis of the kernel of T.
If anyone could clarify what is the difference between the two and how the calculation procedures are different I would also appreciate that.
Thank you very much.