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If $A=(a_{ij})$ is a ${n \times n}$ matrix such that $\forall i,j$ ,$a_{ij}=2i+3j$ then what is the rank of $A$?

I tried this problem but I'm getting nowhere. Is there any direct (or indirect) method to calculate the rank of $A$? Any help will be appreciated. Thanks and regards.

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Hint: What's the difference between consecutive rows (or consecutive columns)? So how many rows (columns) do you need in addition to the first one to generate all the others?

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  • $\begingroup$ @Sayantan: You're welcome. $\endgroup$
    – joriki
    Jan 7 '12 at 16:25

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