Question

求二次型的F（X1，X2，X3）=X1X2+X2X3+X3+X1的矩阵，并用配方法求二次性的标准

Answer 1

简单计算一下即可，答案如图所示

Answer 2

f=x1^2+2x1x2+2x2x3-4x1x3= (x1+x2-2x3)^2-x2^2-4x3^2+6x2x3= (x1+x2-2x3)^2-(x2-3x3)^2+5x3^2= y1^2-y2^2+5y3^2Y=CX,C=1 1 -20 1 -30 0 1C^-1=1 -1 -10 1 30 0 1所用变换为 X=C^-1Y