线性代数,计算题
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/23 18:07:46
线性代数,计算题
![](http://img.wesiedu.com/upload/c/7d/c7d3a13d73bcafeab1d27b986acbef0f.jpg)
![](http://img.wesiedu.com/upload/c/7d/c7d3a13d73bcafeab1d27b986acbef0f.jpg)
按第n列展开
Dn = an (-1)^(1+n) (-x1)(-x2)...(-xn-1) + xnDn-1
= x1x2...xn-1an + xnDn-1 = x1x2...xn-1an + xn( x1x2...xn-2an-1 + xn-1Dn-2 )
= x1x2...xn-1an + x1x2...xn-2an-1xn + xnxn-1Dn-2
= ...(迭代)
= x1x2...xn-1an + x1x2...xn-2an-1xn +...+ x1a2...xn-1xn + xnxn-1...x2D1
= x1x2...xn-1an + x1x2...xn-2an-1xn +...+ x1a2...xn-1xn + a1x2...xn-1xn
Dn = an (-1)^(1+n) (-x1)(-x2)...(-xn-1) + xnDn-1
= x1x2...xn-1an + xnDn-1 = x1x2...xn-1an + xn( x1x2...xn-2an-1 + xn-1Dn-2 )
= x1x2...xn-1an + x1x2...xn-2an-1xn + xnxn-1Dn-2
= ...(迭代)
= x1x2...xn-1an + x1x2...xn-2an-1xn +...+ x1a2...xn-1xn + xnxn-1...x2D1
= x1x2...xn-1an + x1x2...xn-2an-1xn +...+ x1a2...xn-1xn + a1x2...xn-1xn