用配方法化二次型f(x1,x2,x3)=x12+2x1x2+2x1x3-4x32为标准形.

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问题 用配方法化二次型f(x1,x2,x3)=x12+2x1x2+2x1x3-4x32为标准形.

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答案f(x1,x2,x3)=x12+2x1x2+2x1x3-4x32=(x1+x2+x3)2-(x2+x3)2-4x32, 令[*] 则f(x1,x2,x3)=XTAX[*]y12-y22-4y32

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