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Let's call a sequence semi-arithmetic if the difference of any two consecutive elements of it can take two different values only.(E.g the sequence $3,7,11,12,16,17,18$ is semi-arithmetic). For the matrix $A$ it holds that the first three rows of it form a semi-arithmetic sequence and all the other rows of it form an arithmetic sequence. Show that in this case $r(a) \le 9$ where $r$ denotes rank.

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    I wrote exactly as the problem is given.2012-12-10

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