行列の積の具体例

$3$\displaystyle{A= $ \begin{array}{lll}1&5&9& \vspace{6}\\ \end{array} $ }$ , $3$\displaystyle{B= $ \begin{array}{lll}5& \vspace{6}\\ 2& \vspace{6}\\ \end{array} $ }$ , $3$\displaystyle{C= $ \begin{array}{lll}7&4& - 1 & \vspace{6}\\ 3&0&5& \vspace{6}\\ \end{array} $ }$ , $3$\displaystyle{D= $ \begin{array}{lll}5&2& \vspace{6}\\ 3&1& \vspace{6}\\ 4& - 1 & \vspace{6}\\ \end{array} $ }$ , $3$\displaystyle{E= $ \begin{array}{lll}8&4&2& \vspace{6}\\ 1&3& - 6 & \vspace{6}\\ - 7 &0&5& \vspace{6}\\ \end{array} $ }$ のうち，2つの行列が定義されるものについて，その積を求めてみる．

計算:

$3$\displaystyle{AD}$ $3$\displaystyle{= $ \begin{array}{lll}1&5&9& \vspace{6}\\ \end{array} $ $ \begin{array}{lll}5&2& \vspace{6}\\ 3&1& \vspace{6}\\ 4& - 1 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 56 & - 2 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{AE}$ $3$\displaystyle{= $ \begin{array}{lll}1&5&9& \vspace{6}\\ \end{array} $ $ \begin{array}{lll}8&4&2& \vspace{6}\\ 1&3& - 6 & \vspace{6}\\ - 7 &0&5& \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 1\cdot 8+5\cdot 1+9\cdot \( - 7 $ & 1\cdot 4+5\cdot 3+9\cdot 0 & 1\cdot 2+5\cdot $ - 6 $ +9\cdot 5 & \vspace{6}\\ \end{array} \) }$

$3$\displaystyle{= $ \begin{array}{lll} - 50 & 19 & 17 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{BA}$ $3$\displaystyle{= $ \begin{array}{lll}5& \vspace{6}\\ 2& \vspace{6}\\ \end{array} $ $ \begin{array}{lll}1&5&9& \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll}5& 25 & 45 & \vspace{6}\\ 2& 10 & 18 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{CD}$ $3$\displaystyle{= $ \begin{array}{lll}7&4& - 1 & \vspace{6}\\ 3&0&5& \vspace{6}\\ \end{array} $ $ \begin{array}{lll}5&2& \vspace{6}\\ 3&1& \vspace{6}\\ 4& - 1 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 35+12- 4 & 14+4+1 & \vspace{6}\\ 15+0+20 & 6+0- 5 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 43 & 19 & \vspace{6}\\ 35 &1& \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{CE}$ $3$\displaystyle{= $ \begin{array}{lll}7&4& - 1 & \vspace{6}\\ 3&0&5& \vspace{6}\\ \end{array} $ $ \begin{array}{lll}8&4&2& \vspace{6}\\ 1&3& - 6 & \vspace{6}\\ - 7 &0&5& \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 56+4+7 & 28+12+0 & 14- 24- 5 & \vspace{6}\\ 24+0- 35 & 12+0+0 & 6+0+25 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 67 & 40 & - 15 & \vspace{6}\\ - 11 & 12 & 31 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{DB}$ $3$\displaystyle{= $ \begin{array}{lll}5&2& \vspace{6}\\ 3&1& \vspace{6}\\ 4& - 1 & \vspace{6}\\ \end{array} $ $ \begin{array}{lll}5& \vspace{6}\\ 2& \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 29 & \vspace{6}\\ 17 & \vspace{6}\\ 18 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{DC}$ $3$\displaystyle{= $ \begin{array}{lll}5&2& \vspace{6}\\ 3&1& \vspace{6}\\ 4& - 1 & \vspace{6}\\ \end{array} $ $ \begin{array}{lll}7&4& - 1 & \vspace{6}\\ 3&0&5& \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 35+6 & 20+0 & - 5+10 & \vspace{6}\\ 21+3 & 12+0 & - 3+5 & \vspace{6}\\ 28- 3 & 16+0 & - 4- 5 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 41 & 20 &5& \vspace{6}\\ 24 & 12 &2& \vspace{6}\\ 25 & 16 & - 9 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{ED}$ $3$\displaystyle{= $ \begin{array}{lll}8&4&2& \vspace{6}\\ 1&3& - 6 & \vspace{6}\\ - 7 &0&5& \vspace{6}\\ \end{array} $ $ \begin{array}{lll}5&2& \vspace{6}\\ 3&1& \vspace{6}\\ 4& - 1 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 40+12+8 & 16+4- 2 & \vspace{6}\\ 5+9- 24 & 2+3+6 & \vspace{6}\\ - 35+0+20 & - 14+0- 5 & \vspace{6}\\ \end{array} $ }$

$3$\displaystyle{= $ \begin{array}{lll} 60 & 18 & \vspace{6}\\ 21 & 11 & \vspace{6}\\ - 15 & - 19 & \vspace{6}\\ \end{array} $ }$

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最終更新日： 2023年2月9日