每週問題 October 8, 2012

$A, B$ 是實矩陣，證明：若 $N(A^T)\subseteq N(B^T)$，則 $C(B)\subseteq C(A)$

Let $A$ and $B$ be an $m\times n$ and $m\times p$ real matrices, respectively. If $N(A^T)\subseteq N(B^T)$, prove that $C(B)\subseteq C(A)$.

$(N(A^T)+N(B^T))^\perp\subseteq N(A^T)^\perp\cap N(B^T)^\perp$

PowSol-Oct-8-12