用配方法将该二次型化为标准型:2x1x2+2x2x3+2x1x3
答案:2 悬赏:30
解决时间 2021-01-24 03:54
- 提问者网友:相思似海深
- 2021-01-23 20:37
用配方法将该二次型化为标准型:2x1x2+2x2x3+2x1x3
最佳答案
- 二级知识专家网友:何以畏孤独
- 2021-01-23 22:11
f=2x1x2-2x1x3-6x2x3
= 2(y1+y2)(y1-y2)-2(y1+y2)y3-6(y1-y2)y3
= 2y1^2 - 8y1y3 - 2y2^2 + 4y2y3
= 2(y1-2y3)^2 - 2y2^2 + 4y2y3 - 8y3^2
= 2(y1-2y3)^2 - 2(y2-y3)^2 - 6y3^2
= 2z1^2-2z2^2-6z3^2
= 2(y1+y2)(y1-y2)-2(y1+y2)y3-6(y1-y2)y3
= 2y1^2 - 8y1y3 - 2y2^2 + 4y2y3
= 2(y1-2y3)^2 - 2y2^2 + 4y2y3 - 8y3^2
= 2(y1-2y3)^2 - 2(y2-y3)^2 - 6y3^2
= 2z1^2-2z2^2-6z3^2
全部回答
- 1楼网友:逐風
- 2021-01-23 23:02
=(x1+x2+x3)^2 - x1^2 - x2^2 - x3^2
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