SEEMOUS 2010- problema 4

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Radu Titiu
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SEEMOUS 2010- problema 4

Post by Radu Titiu »

Fie \( A \) si \( B \) \( \in \mathcal{M}_n(\mathbb{Z}) \) cu \( \det(B) \neq 0 \).Aratati ca exista \( m \in \mathbb{N} \) a.i.

\( AB^{-1} = \sum_{k=1}^n N_k^{-1} \)

unde \( N_k \in \mathcal{M}_n(\mathbb{Z}) \) si \( N_i \neq N_j \) daca \( i\neq j \).

(Obs: \( B^{-1} si N_k^{-1} \) pot avea elemente din \( \mathbb{Q} \))
A mathematician is a machine for turning coffee into theorems.
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