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ALSON
Lv 4
ALSON asked in 科學數學 · 1 decade ago

線性代數的問題│很急很急│拜託幫忙!!!│感謝│20點

┌ 3 2 5 9 ┐

Assume A= │-1 3 2 -3│

│ 2 1 4 7│

└-4 -2 -8 -14┘

(a)what is the dimension of the column space W?

(b)Find a lasis for W⊥

(c)Find a lasis for the nullspace of A

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  • 小偉
    Lv 6
    1 decade ago
    Favorite Answer

    (a) [ 1 0 -2 0 ]

    [ 0 1 1 0 ]

    A經列運算簡化後得 [ 0 0 1 1 ]

    [ 0 0 0 0 ]

    所以 Rank(A)=3 則 Dim(W)=3

    (b)Null(A)={x |Ax=0}

    [x1] [ 1 0 -2 0 ][x1]

    [x2] [ 0 1 1 0 ][x2]

    let x=[x3] and Ax=0, then [ 0 0 1 1 ][x3] =0

    [x4] [ 0 0 0 0 ][x4]

    [ 2] [ 2]

    [-1] [-1]

    let x1=t then x= t[ 1]. let v=[ 1] then W⊥=spn(v)

    [-1] [-1]

    (c) Dim(Null(A))=Dim(V)-Dim(W)=1

    so. Null(A)=W⊥=spn(v)

    Source(s): 小偉10年前學的
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