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Matrix multiplication:
Enter two matrices that can be multiplied, with each element separated by a comma and each row ending with a semicolon.
Note that mathematical functions and variables are not supported.
Enter two matrices that can be multiplied, with each element separated by a comma and each row ending with a semicolon.
Note that mathematical functions and variables are not supported.
Current location：Linear algebra >Matrix multiplication >History of matrix multiplication >Answer
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &123\ &234\ &345\ \\ &456\ &567\ &678\ \\ &789\ &890\ &901\ \end{pmatrix}\times \begin{pmatrix} &111\ &222\ &333\ \\ &444\ &555\ &666\ \\ &777\ &888\ &999\ \end{pmatrix}}\\ \\Solution:&\\&\begin{pmatrix} &123\ &234\ &345\ \\ &456\ &567\ &678\ \\ &789\ &890\ &901\ \end{pmatrix}\times \begin{pmatrix} &111\ &222\ &333\ \\ &444\ &555\ &666\ \\ &777\ &888\ &999\ \end{pmatrix}\\\\=\ \ &\begin{pmatrix} &385614\ &463536\ &541458\ \\ &829170\ &1017981\ &1206792\ \\ &1182816\ &1469196\ &1755576\ \end{pmatrix}\end{aligned}$$
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The properties of matrix multiplication:
(i) Combining Law: （A b）C=A（b C）
(ii) Distribution Law: A ( B + C ) = A B + A C either or ( A + B ) C = A C + B C .
(iii) λ ( A B ) = ( λ A ) B = A ( λ B ) .
Among them, A, B, and C are the matrices that make the multiplication of the above matrices meaningful, λ It's a number.