f(x1,x2,x3)=x1^2+2x2^2+7x3^2+2x1x2+4x2x3
= (x1+x2)^2+x2^2+7x3^2+4x2x3
= (x1+x2)^2+(x2+2x3)^2+3x3^2
令扒旁槐启芹 C=
1 1 0
0 1 2
0 0 1
Y=CX, 则有春友
f = y1^2+y2^2+3y3^2
如二次型f(x1,x2,x3)=x1²+2x2²+7x3²+2x1x2+4x2x3化为标型，写出所有可逆线性变换。
f(x1,x2,x3)=x1^2+2x2^2+7x3^2+2x1x2+4x2x3
= (x1+x2)^2+x2^2+7x3^2+4x2x3
= (x1+x2)^2+(x2+2x3)^2+3x3^2
令扒旁槐启芹 C=
1 1 0
0 1 2
0 0 1
Y=CX, 则有春友
f = y1^2+y2^2+3y3^2