## 每週問題 June 6, 2016

Let $A$ be an $m\times n$ complex matrix. If $A\mathbf{x}=\mathbf{b}$ is consistent for some $\mathbf{b}$, prove that there exists a unique solution $\mathbf{x}$ in the column space of $A^\ast$.

$\displaystyle A\mathbf{x}=A(\mathbf{y}+\mathbf{z})=A\mathbf{y}+A\mathbf{z}=A\mathbf{y}=\mathbf{b}$