Let A = and by T(X) = AX.

Find eigenpairs for A, find a basis for Ker(T) using the eigenvectors previously found, find a basis for Im(T) using eigenvectors previously found.

The eigenpairs I got were...

(0, ), (1, ), and (2,

I wasn't sure about the Kernel or Image parts but for the kernel I got

t

And for the image I got

Could someone please verify if this is correct or not? I assume the kernel and image are not so could someone also please help me with that?

Thanks