If the system of equation \(2\mathrm{x}+\mathrm{λy}+3\mathrm{z}=5\\ 3\mathrm{x}+2\mathrm{y}-\mathrm{z}=7\\ 4\mathrm{x}+5…

If the system of equation
\(2\mathrm{x}+\mathrm{λy}+3\mathrm{z}=5\\ 3\mathrm{x}+2\mathrm{y}-\mathrm{z}=7\\ 4\mathrm{x}+5\mathrm{y}+\mathrm{μz}=9\)
has infinitely many solutions, then \(\left({\lambda }^{2}+{\mu }^{2}\right)\) is equal to :

[JEE Main 2025, 2 Apr (Shift 2)]