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Found problems: 1

2006 Mathematics for Its Sake, 2
Tags: linear algebra equation , matrix equation , matrix , induction , linear algebra
Let be a natural number $ n. $ Solve in the set of $ 2\times 2 $ complex matrices the equation $$ \begin{pmatrix} -2& 2007\\ 0&-2 \end{pmatrix} =X^{3n}-3X^n. $$ [i]Petru Vlad[/i]