I am teaching a mostly "no proofs" linear algebra for engineers. So there is no time to explain that injectivity and surjectivity are dual properties in terms of left/right cancellability or vanishing of kernel/cokernel. 1/2
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Of course, all this would be clearer if we were allowed to talk about dual spaces. But alas, while we can talk about the transpose of a matrix, we cannot interpret it as the matrix of the transpose of the original map.
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