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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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &37\ &23\ &46\ &35\ \\ &52\ &36\ &39\ &89\ \\ &74\ &46\ &34\ &25\ \\ &47\ &47\ &82\ &59\ \end{pmatrix}\times \begin{pmatrix} &2\ &3\ &4\ &5\ \\ &6\ &2\ &7\ &3\ \\ &9\ &99\ &5\ &3\ \\ &1\ &2\ &9\ &83\ \end{pmatrix}}\\ \\Solution:&\\&\begin{pmatrix} &37\ &23\ &46\ &35\ \\ &52\ &36\ &39\ &89\ \\ &74\ &46\ &34\ &25\ \\ &47\ &47\ &82\ &59\ \end{pmatrix}\times \begin{pmatrix} &2\ &3\ &4\ &5\ \\ &6\ &2\ &7\ &3\ \\ &9\ &99\ &5\ &3\ \\ &1\ &2\ &9\ &83\ \end{pmatrix}\\\\=\ \ &\begin{pmatrix} &661\ &4781\ &854\ &3297\ \\ &760\ &4267\ &1456\ &7872\ \\ &755\ &3730\ &1013\ &2685\ \\ &1173\ &8471\ &1458\ &5519\ \end{pmatrix}\end{aligned}$$
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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.