分别用配方法和初等变换法把二次型化为标准形f(x1,x2,x3) = x1^2+5x2^2-4x3^2+2x1x2-4x1x3_数学解答

分别用配方法和初等变换法把二次型化为标准形
f(x1,x2,x3) = x1^2+5x2^2-4x3^2+2x1x2-4x1x3

人气：184 ℃　时间：2020-08-24 22:20:30

解答

f = x1^2+5x2^2-4x3^2+2x1x2-4x1x3= (x1+x2-2x3)^2+4x2^2-8x3^2+4x2x3= (x1+x2-2x3)^2+4(x2+(1/2)x3)^2-9x3^2= y1^2+4y2^2-9y3^2Y=CX,X=C^-1YC =1 1 -20 1 1/20 0 1P = C^-1 =1 -1 5/20 1 -1/20 0 1初等变换法1 1 -2...