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$A$ is an $n\times n$ matrix and rank$(A)=r$.,$B,C$ are both $n \times n$ matrices and $AB=AC.$ Calculate the maximun possible rank of the matrix $(B-C)$.

This question is a part of my homework in Linear Algebra, and the title of the homework is "Vector spaces, Linear dependence, Span, and Basis". I have no clue/direction of how to approch this question.

Thank you!

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    Deal with the case $A=\operatorname{Diag}(\underbrace{1,\dots,1}_{r\mbox{ times }},\underbrace{0,\dots, 0}_{n-r\mbox{ times}})$.2012-12-01

2 Answers 2