a)Aratati ca pentru orice matrice \( A \in \mathcal{M}_2(\mathbb{R}) \) exista \( B,C \in \mathcal{M}_2(\mathbb{R}) \) a.i. \( A=B^2+C^2 \).
b) nu exista \( B,C \in \mathcal{M}_2(\mathbb{R}) \) a.i. \( BC=CB \) si \( \begin{pmatrix} 0 & 1 \\ 1 & 0\end{pmatrix}=B^2+C^2 \).
SEEMOUS 2010- problema 3
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SEEMOUS 2010- problema 3
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