1. ## Image and kernal

Hi could some please just help me to find the image and kernal of the linear transformation and i should be able to prove the rest.

thanks

2. Do you understand that you do not need to, and, indeed, are not expected to actually find the image and kernel in order to do this? You are told that $T^2(v)= T(T(v))= 0$ for every v in the vector space. There are an infinite number of functions, T, that will do that and they have different images and kernels. In order to prove that, for such a function, $Im(T)\subseteq Ker(T)$ you just need to know the definitions of "image" and "kernel".

3. Hi, i just tryed the proof,

Know $T(v)=Im(T)$.
So
$T^2(v)= T(T(v))=T(Im(T))=0$

Thus image is a subset of the kernal

4. Hi, i just tryed the proof,

Know $T(v)=Im(T)$ .

So

$T^2(v)= T(T(v))=T(Im(T))=0$

Thus image is a subset of the kernal

5. is what i wrote above correct?