解答题
设二次型f(x1,x2,x3)=
+
+
+2ax1x2+2ax1x3+2ax2x3,经过可逆线性变换
=
得g(y1,y2,y3)=
+
+
+++2ax1x2+2ax1x3+2ax2x3,经过可逆线性变换=得g(y1,y2,y3)=++
【正确答案】解：(Ⅰ)f(x1,x2,x3)的二次型矩阵, g(y1,y2,y3)的二次型矩阵,显然r(B)=2,f(x1,x2,x3)经可逆线性变换x=Py变换为g(y1,y2,y3),则r(A)=r(B)=2,得a=1或a=,当a=1时,r(A)=1,故a=1(舍去),则a=; (Ⅱ)当a=时, 又g(y1,y2,y3)= 即矩阵
【答案解析】