Question

化二次型f(x1,x2,x3)=x1的平方-3x2的平方-2x1x2+2x1x1-6x2x3为标准型

Answer 1

f(x1,x2,x3)
= x1^2-3x2^2-2x1x2+2x1x3-6x2x3
= (x1-x2+x3)^2-4x2^2-x3^2-4x2x3
= (x1-x2+x3)^2-4(x2+(1/2)x3)^2
= (x1-x2+x3)^2-(2x2+x3)^2
= y1^2-y2^2.