Gazeta matematică 2022: Difference between revisions

Revision as of 08:02, 20 July 2024

Gazeta Matematică 3/2022

S:L22.108. (Nicolae Mușuroia)

Fie 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 A, B \in \mathcal{M}_3 \left( \mathbb{R}\right)} cu 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 AB = BA} , 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 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) = \alpha \cdot \det(B) \ne 0} , unde 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 \alpha \ne 1.}

__FORTEAZACUPRINS__

@@ Line 3: / Line 3: @@
 '''S:L22.108. (Nicolae Mușuroia)'''
-''Fie <math>A, B \in \mathcal{M}_3 (\mathbb{R})</math> cu <math>AB = BA</math>, <math>A^2+B^2</math> neinversabilă și <math>det⁡(A)=α det⁡(B)≠0</math>, unde <math>α≠1<math/>. Arătați  că <math display="block">\frac{\det⁡(A+B)}{\det⁡(A-B)} = \frac{\det⁡(A) + \det⁡(B)}{\det⁡(A)-\det⁡(B)}.</math>
+''Fie <math>A, B \in \mathcal{M}_3 \left( \mathbb{R}\right)</math> cu <math>AB = BA</math>, <math>A^2+B^2</math> neinversabilă și <math>\det(A) = \alpha \cdot \det(B) \ne 0</math>, unde <math>\alpha \ne 1.</math>''
+__FORTEAZACUPRINS__