Question

设三元二次型f（x1,x2,x3）=X1²+X2²+X3²-2X1X2-4X1X3+2X2X3用配方

法将该二次型化为标准型？老师快考试了，给我解解吧

Answer 1

f(x1,x2,x3)=x1^2+x2^2+x3^2-2x1x2-4x1x3+2x2x3
= (x1-x2-2x3)^2-3x3^2-2x2x3
= (x1-x2-2x3)^2-3(x3+(1/3)x2)^2+(1/3)x2^2
= y1^2-3y2^2+(1/3)y3^2

Answer 2

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