Linear Algebra I · Quotient spaces and universal factorization
Evaluating a map induced on a quotient
Problem
Let $T:V\to W$ be linear and assume $N\subseteq\ker T$. Let $\overline T:V/N\to W$ be induced by $\overline T(x+N)=T(x)$. Prove this evaluation identity for every $x$.
Hint
Write the input as the class represented by $x$.
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