1. Rows and Columns

$$\{\begin{array}{l}2x+3y+z=1\\ 5x+z=3\\ 9y+4z=7\end{array}$$

위와 같은 선형연립방정식을 해석할 때 두 가지 관점이 있다.

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Row concept

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Column concept

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Basic multiplication

Matrix에 multiplication을 할 때 Column기준이 있고 Row기준이 있다.

Column:

$$\left[\begin{array}{clr}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=x\left[\begin{array}{c}1\\ 4\\ 7\end{array}\right]+y\left[\begin{array}{c}2\\ 5\\ 8\end{array}\right]+z\left[\begin{array}{c}3\\ 6\\ 9\end{array}\right]$$

 

Row:

$$\left[\begin{array}{clr}x& y& z\end{array}\right]\left[\begin{array}{clr}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]=\begin{array}{c}x[\begin{array}{clr}1& 2& 3\end{array}]\\ +\\ y[\begin{array}{clr}4& 5& 6\end{array}]\\ +\\ z[\begin{array}{clr}7& 8& 9\end{array}]\end{array}$$