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Soient \(A \in \mathcal{M}_{n,p}(K)\) et \(B \in \mathcal{M}_{n,q}(K)\). On considère \(C = (A\ B) \in \mathcal{M}_{n,p+q}(K)\).
Montrer que : \(\mathrm{rg}(C) = \mathrm{rg}(A) \Leftrightarrow \exists\ P \in \mathcal{M}_{p,q}(K)\) tq \(B = AP\).
Soient \(A \in \mathcal{M}_{n,p}(K)\) et \(B \in \mathcal{M}_{n,q}(K)\). On considère \(C = (A\ B) \in \mathcal{M}_{n,p+q}(K)\).
Montrer que : \(\mathrm{rg}(C) = \mathrm{rg}(A) \Leftrightarrow \exists\ P \in \mathcal{M}_{p,q}(K)\) tq \(B = AP\).