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A question about findind an operator that

  1. Mar 7, 2008 #1
  2. jcsd
  3. Mar 7, 2008 #2


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    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.
    Last edited: Mar 8, 2008
  4. Mar 8, 2008 #3
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