用配方法化二次型为标准型,f(x1,x2,x3)=x1x2-x1x3-3x2x3
问题描述：
用配方法化二次型为标准型,f(x1,x2,x3)=x1x2-x1x3-3x2x3
答
f(x1,x2,x3)=x1x2-x1x3-3x2x3
=(y1+y2)(y1-y2)-(y1+y2)y3-3(y1-y2)y3
=y1^2 - 4y1y3 - y2^2 + 2y2y3
=(y1-2y3)^2 - y2^2 + 2y2y3 - 4y3^2
=(y1-2y3)^2 - (y2-y3)^2 - 3y3^2
=z1^2-z2^2-3z3^2