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I forgot how to prove the following inequality. Could anybody help?

Let $A, B, C$ be matrices of appropriate dimensions: $$rank\left( \left[\begin{array}{rr} A & 0\\ C & B \end{array}\right]\right)\ge rank\left( \left[\begin{array}{rr} A & 0\\ 0 & B \end{array}\right]\right).$$

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    What does rank-nullity imply?2011-04-15
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    @ehsanmo: does rank-nullity imply this directly? If so, please post an answer with such reasoning. I do not see this argument.2011-04-19

3 Answers 3