# Image and kernal

• Oct 30th 2010, 05:08 AM
nerdo
Image and kernal
Attachment 19527

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
• Oct 30th 2010, 05:25 AM
HallsofIvy
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 \$\displaystyle 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, \$\displaystyle Im(T)\subseteq Ker(T)\$ you just need to know the definitions of "image" and "kernel".
• Oct 30th 2010, 06:00 AM
nerdo
Hi, i just tryed the proof,

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

Thus image is a subset of the kernal
• Oct 30th 2010, 06:08 AM
nerdo
Hi, i just tryed the proof,

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

So

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

Thus image is a subset of the kernal
• Nov 1st 2010, 11:51 AM
nerdo
is what i wrote above correct?