(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let F : M_{nn}(R) → R where F(A) =tr(A). Show that F is a linear transformation. Find the kernel of F as well as its dimension. What is the image of F?

2. Relevant equations

3. The attempt at a solution

I have shown that it is a linear transformation. But I am not sure about the Ker(F) and Im(F),

would Ker(F) just be {tr(A), for A in M_{nn}}? And would the Im(F) just be {a : a[itex]\in[/itex]ℝ}? Thanks.

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# Homework Help: Find the Kernel of the Trace of a Matrix

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