Matrix - own

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nayel
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Matrix - own

Unread post by nayel » Tue Jun 12, 2012 6:06 am

Let $A$ be an $n\times n$ real matrix ($n\in\mathbb N$). Suppose that all entries in the first column of $A^n$ are zero, but not all entries in the first column of $A^{n-1}$ are zero. Prove that all entries of $A^n$ are zero.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein

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