作者tibicos (tibicos)
看板Math
标题Re: [线代] orthogonal complement
时间Mon Jun 6 21:56:08 2011
※ 引述《mqazz1 (无法显示)》之铭言：
: find the orthogonal complement of the subspace of R^3 spanned by
: (1, 2, 1)^T and (1, -1, 2)^T
: =================================================================
: 我这样写
: [a] [1] [a] [ 1]
: <[b],[2]> = 0 <[b],[-1]> = 0
: [c],[1] [c] [ 2]
: 解联立 c = 3b
: [ a] [1] [0]
: span{[ b]} => span{[0], [1]}
: [3b] [0] [3]
: 解答是(-5, 1, 3)^T
: 请问我是什麽地方错了?
: 谢谢!!
可令
A=[ 1 2 1]
[ 1 -1 2]
则您要求的恰好是N(A)
先求A之reduced row echelon form (rref) R=[1 0 5/3]
[0 1 -1/3]
就可看出N(A)=span([-5/3 1/3 1]^T)
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 111.252.9.218
1F：→ mqazz1 :谢谢!! 06/07 00:02