#940 · Algebra · Linear equations

Eliminant of a symmetric system

Show that the eliminant (determinant condition) of the system $a x + cy + b z = 0, c x + b y + a z = 0, b x + a y + cz = 0$ is $a^{3} + b^{3} + c^{3} - 3 ab c = 0$ .

~12 minProof · checked by AIdeterminantsymmetry

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 16

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