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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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &4\ &2\ &4\ &2\ \\ &8\ &16\ &8\ &4\ \\ &32\ &64\ &128\ &16\ \\ &256\ &512\ &2048\ &4096\ \end{pmatrix}\times \begin{pmatrix} &4\ &2\ &4\ &2\ \\ &8\ &16\ &8\ &4\ \\ &32\ &64\ &128\ &16\ \\ &256\ &512\ &2048\ &4096\ \end{pmatrix}}\\ \\Solution:&\\&\begin{pmatrix} &4\ &2\ &4\ &2\ \\ &8\ &16\ &8\ &4\ \\ &32\ &64\ &128\ &16\ \\ &256\ &512\ &2048\ &4096\ \end{pmatrix}\times \begin{pmatrix} &4\ &2\ &4\ &2\ \\ &8\ &16\ &8\ &4\ \\ &32\ &64\ &128\ &16\ \\ &256\ &512\ &2048\ &4096\ \end{pmatrix}\\\\=\ \ &\begin{pmatrix} &672\ &1320\ &4640\ &8272\ \\ &1440\ &2832\ &9376\ &16592\ \\ &8832\ &17472\ &49792\ &67904\ \\ &1119232\ &2236928\ &8655872\ &16812544\ \end{pmatrix}\end{aligned}$$
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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.