Re: [線代] orthogonal complement

[tibicos (tibicos)]

※ 引述《mqazz1 (無法顯示)》之銘言：
: find the orthogonal complement of the subspace of R^3 spanned by
: (1, 2, 1)^T and (1, -1, 2)^T
: =================================================================
: 我這樣寫
:  [a] [1]                 [a] [ 1]
: <[b],[2]> = 0           <[b],[-1]> = 0
:  [c],[1]                 [c] [ 2]
: 解聯立 c = 3b
:      [ a]          [1]  [0]
: span{[ b]} => span{[0], [1]}
:      [3b]          [0]  [3]
: 解答是(-5, 1, 3)^T
: 請問我是什麼地方錯了?
: 謝謝!!

可令
    A=[ 1  2 1]
      [ 1 -1 2]

   則您要求的恰好是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)

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→ mqazz1      :謝謝!!