Mathematics, 16.01.2020 07:31 lexybellx3
In matrix multiplication, such as ab=c, the columns of b form the rows of c. why is this?
Answers: 1
![\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right] = \left[\begin{array}{cc} a_{11}b_{11} + a_{12}b_{21} & a_{11}b_{12} + a_{12}b_{22} \\ a_{21}b_{11} + a_{22}b_{21} & a_{21}b_{12} + a_{22} b_{22} \end{array}\right]](/tpl/images/0457/4643/a32f2.png)
![\begin{array}{ccc} {} & [1] & [2] \\ 1| &1 & 2 \\ 2| & 2 &4 \end{array}](/tpl/images/0457/4643/0d37f.png)
![\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right]](/tpl/images/0457/4643/af6f4.png)
![= \begin{array}{cc} {} & \left[\begin{array}{cc} b_{11} & b_{12}\end{array} \right]\\ \left[\begin{array}{c} a_{11} \\ a_{21} \end{array} \right] \end{array} +\begin{array}{cc} {} & \left[\begin{array}{cc} b_{21} & b_{22}\end{array} \right]\\ \left[\begin{array}{c} a_{12} \\ a_{22} \end{array} \right] \end{array}](/tpl/images/0457/4643/e2d0c.png)
![= \left[\begin{array}{cc} a_{11} b_{11} & a_{11} b_{12} \\ a_{21} b_{11} & a_{21} b_{12} \end{array} \right] + \left[\begin{array}{cc} a_{12} b_{21} & a_{12} b_{22} \\ a_{22} b_{21} & a_{22} b_{22} \end{array} \right]](/tpl/images/0457/4643/a5ae7.png)
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