Is is true that if $A$ is an $m \times n$ matrix and if $A\vec{x}=A\vec{y}$ then $\vec{x}=\vec{y}$? Intuitively this makes sense to me, but I'm just looking for verification or contradiction.
2026-04-13 19:12:26.1776107546
Basic Matrix Equality
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Counterexample:
Let $A$ be the zero matrix of size $m \times n$, then we have $Ax= Ay$ for any $x$ and $y$.