作者powerkshs (氣質斯文讀書人)
看板Math
標題Re: [線代] rank
時間Thu Apr 7 11:34:15 2011
"=>"
Suppose not,
then
｜ a11 a12｜ ｜a11 a13｜ ｜ a12 a13｜
｜ a21 a22｜,｜a21 a23｜, ｜ a22 a23｜ is allzero
→rank(A)=0 or 1 →←
∴at least one of ｜ a11 a12｜ ｜a11 a13｜ ｜ a12 a13｜ is nonzero
｜ a21 a22｜,｜a21 a23｜, ｜ a22 a23｜
"<="
∵ at least one of ｜ a11 a12｜ ｜a11 a13｜ ｜ a12 a13｜ is nonzero
｜ a21 a22｜,｜a21 a23｜, ｜ a22 a23｜
∴rank(A)≧2
又∵矩陣Ａ是2*3
∴rank(A)≦2
∴rank(A)=2
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