Show that the system of linear equations has a non-trivial solution $\leftrightarrow$ $\alpha = \beta$
$$x+y+\alpha.z=0$$ $$x+y+\beta.z=0$$ $$\alpha.x+\beta.y+z=0$$
How could it be demonstrated?
2026-04-18 02:53:43.1776480823
Show that the system of linear equations has a non-trivial solution
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The determinant of the coefficient matrix is $-(\alpha -\beta)^{2}$ which is $0$ iff $\alpha =\beta$.