Linear Algebra I · Quotient spaces and universal factorization
Constructing the second-isomorphism map
Problem
For subspaces $N,P\le V$, construct the linear equivalence $P/(P\cap N)\to(P+N)/N$ and prove it sends the class of $p\in P$ to the class of $p$ modulo $N$.
Hint
Compose the inclusion $P\hookrightarrow P+N$ with projection modulo $N$.
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