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- Feb 5, 2012

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Here's a question I found on a Wiki book.

**Question:**The matrix \(T\) is \(5\times 5\) with the single eigenvalue 3. The nullities of the powers are: \((T-3I)\) has nullity two, \((T-3I)^2\) has nullity three, \((T-3I)^3\) has nullity four, and \((T-3I)^4\) has nullity five. Find the Jordan Normal form from the given date.

So I can understand that since the nullity of \((T-3I)\) is two there are two Jordan blocks. However I still don't get how exactly we can calculate the sizes of those Jordan blocks from the above data. Can anybody guide me through this process please?