#1503 · Algebra · Linear equations

Quadratic form ratios

If $a x + h y + g z = 0$ , $h x + b y + f z = 0$ , $g x + f y + cz = 0$ , prove that
$\frac{x ^{2}}{b c - f ^{2}} = \frac{y ^{2}}{c a - g ^{2}} = \frac{z ^{2}}{ab - h ^{2}} .$

~18 minProof · checked by AIdeterminantssymmetry

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 28 (part 1)

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