- Thread starter
- #1

- Feb 5, 2012

- 1,621

Take a look at this question.

Now the problem is that I feel this question is not properly worded. If the linear transformations have rank = 1 then it is obvious that \(\mbox{Im f}=\mbox{Im g}=\{0\}\). So restating that is not needed. Don't you think so? Correct me if I am wrong. If I am correct the answer is also obvious. Since the image space of the linear transformations contain only the identity element, \(fg=gf\).Show that if two linear transformations \(f,\,g\) of rank 1 have equal \(\mbox{Ker f}=\mbox{Ker g},\,\mbox{Im f}=\mbox{Im g},\) then \(fg=gf\).