Thursday, February 22, 2018

linear algebra - Prove that elementary matrices perform row operations

How to prove that elementary matrices actually perform their intended row operations: multiplying by a constant, adding a multiple of one row to another, and switching two rows?




I've seen examples of their use, but I haven't seen a proof for an $n$ by $n$ matrix.

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analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...