## 每週問題 September 23, 2013

Let $A=\begin{bmatrix} P\\ Q \end{bmatrix}$ be an $n\times n$ real matrix. If $N(P)=C(Q^T)$, show that $A$ is nonsingular. Note that $N(P)$ is the nullspace of $P$ and $C(Q^T)$ is the column space of $Q^T$.

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