A triangle is bounded by the lines a1x+b1y+c1=0, a2x+b2y+c2=0 and a2x+b2y+c2=0.
Show that its area, disregarding sign, is
2(a2b3−a3b2)(a3b1−a1b3)(a1b2−a2b1)Δ2,
where Δ is the discriminant of the matrix
M=a1a2a3b1b2b3c1c2c3. Putnamgeometrylinear algebramatrix