Gazeta matematică 2022

Gazeta Matematică 3/2022

S:L22.108. (Nicolae Mușuroia)

Fie Failed to parse (syntax error): {\displaystyle A, B \in \mathcal{M}_3 (\mathbb{R})} cu $AB=BA$, $A^{2}+B^{2}$ neinversabilă și Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle det⁡(A)=α det⁡(B)≠0} , unde Failed to parse (syntax error): {\displaystyle α≠1<math/>. Arătați că <math display="block">\frac{\det⁡(A+B)}{\det⁡(A-B)} = \frac{\det⁡(A) + \det⁡(B)}{\det⁡(A)-\det⁡(B)}.}