A question about findind an operator that

[transgalactic]

follows that rule
http://img89.imageshack.us/my.php?image=69861155mz7.jpg

the problem is that is a fundamental law in spaces
there is no way i can find an operator
that contradicts that

 

[Dick]

You should notice the fine print. The question doesn't say dim(Ker(S))+dim(Im(S))=dim(M2x2). That's the LAW. It says Ker(S)+Im(S)=M2x2. Suppose the matrix m is [[0,1],[0,0]] and S(x)=x*m. Show Ker(S)+Im(S) is 2 dimensional and doesn't span M2x2. I'd almost consider this a trick question.

 

[transgalactic]

thanks