作者dreamfire (梦想之火)
看板Math
标题Re: [线代] 线代(15)
时间Mon Sep 5 00:47:05 2005
※ 引述《PttFund (批踢踢基金只进不出)》之铭言：
: 试求
: [ 1 0 0 0 0 ... 0 ]
: [ -2 1 0 0 0 ... 0 ]
: [ 0 -2 1 0 0 ... 0 ]
: [ 0 0 -2 1 0 ... 0 ]
: [ . . . . . ... . ]
: [ 0 ... 0 0 -2 1 0 ]
: [ 0 ... 0 0 0 -2 1 ]
: 的反矩阵.
Ans:
Let
[ 1 0 0 0 ... 0 0 0 ]
[ -2 1 0 0 ... 0 0 0 ]
[ 0 -2 1 0 ... 0 0 0 ]
[ 0 0 -2 1 ... 0 0 0 ] = A
[ . . . . ... . . . ]
[ 0 0 0 0 ... -2 1 0 ]
[ 0 0 0 0 ... 0 -2 1 ]
If A is a matrix with order n
Then
[ 1 0 0 ... 0 ]
[ -2 1 0 ... 0 ]
[ (-2)^2 -2 1 ... 0 ]
A^(-1)=[ (-2)^3 (-2)^2 -2 ... 0 ]
[ . . . . ]
[ (-2)^(n-1) (-2)^(n-2) (-2)^(n-3) ... 1 ]
#
(Hint: 利用归综法)
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