I have to explain why there does not exist a linear transformation T from $ℝ^5$ to $ℝ^5$ with range(T)=kernel(T).
I know the answer has something to do with dimensions because dim(range(T))+dim(ker(T))=dim(v), but I'm not sure how to explain this.
2026-03-28 10:03:26.1774692206
Explain why there does not exist a linear transformation
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if you want $ker=range$ then, by theorem, dimension of V would be even