Re: [線代] rank

[powerkshs (氣質斯文讀書人)]

"=>"

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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