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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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &8\ &6\ &9\ &3\ &6\ &8\ &4\ \\ &7\ &3\ &6\ &2\ &1\ &7\ &5\ &8\ \\ &2\ &8\ &6\ &9\ &4\ &5\ &2\ &1\ \\ &4\ &2\ &9\ &7\ &7\ &6\ &8\ &2\ \\ &1\ &8\ &3\ &8\ &5\ &9\ &4\ &2\ \\ &9\ &5\ &9\ &4\ &3\ &7\ &4\ &2\ \\ &3\ &9\ &6\ &4\ &3\ &9\ &6\ &5\ \\ &1\ &5\ &3\ &8\ &6\ &4\ &2\ &8\ \end{pmatrix}\times \begin{pmatrix} &1\ &8\ &6\ &9\ &3\ &6\ &8\ &4\ \\ &7\ &3\ &6\ &2\ &1\ &7\ &5\ &8\ \\ &2\ &8\ &6\ &9\ &4\ &5\ &2\ &1\ \\ &4\ &2\ &9\ &7\ &7\ &6\ &8\ &2\ \\ &1\ &8\ &3\ &8\ &5\ &9\ &4\ &2\ \\ &9\ &5\ &9\ &4\ &3\ &7\ &4\ &2\ \\ &3\ &9\ &6\ &4\ &3\ &9\ &6\ &5\ \\ &1\ &5\ &3\ &8\ &6\ &4\ &2\ &8\ \end{pmatrix}}\\ \\Solution:&\\&\begin{pmatrix} &1\ &8\ &6\ &9\ &3\ &6\ &8\ &4\ \\ &7\ &3\ &6\ &2\ &1\ &7\ &5\ &8\ \\ &2\ &8\ &6\ &9\ &4\ &5\ &2\ &1\ \\ &4\ &2\ &9\ &7\ &7\ &6\ &8\ &2\ \\ &1\ &8\ &3\ &8\ &5\ &9\ &4\ &2\ \\ &9\ &5\ &9\ &4\ &3\ &7\ &4\ &2\ \\ &3\ &9\ &6\ &4\ &3\ &9\ &6\ &5\ \\ &1\ &5\ &3\ &8\ &6\ &4\ &2\ &8\ \end{pmatrix}\times \begin{pmatrix} &1\ &8\ &6\ &9\ &3\ &6\ &8\ &4\ \\ &7\ &3\ &6\ &2\ &1\ &7\ &5\ &8\ \\ &2\ &8\ &6\ &9\ &4\ &5\ &2\ &1\ \\ &4\ &2\ &9\ &7\ &7\ &6\ &8\ &2\ \\ &1\ &8\ &3\ &8\ &5\ &9\ &4\ &2\ \\ &9\ &5\ &9\ &4\ &3\ &7\ &4\ &2\ \\ &3\ &9\ &6\ &4\ &3\ &9\ &6\ &5\ \\ &1\ &5\ &3\ &8\ &6\ &4\ &2\ &8\ \end{pmatrix}\\\\=\ \ &\begin{pmatrix} &190\ &244\ &294\ &254\ &179\ &303\ &224\ &182\ \\ &135\ &245\ &234\ &257\ &151\ &240\ &177\ &167\ \\ &162\ &186\ &249\ &219\ &148\ &245\ &190\ &132\ \\ &151\ &292\ &282\ &298\ &188\ &310\ &220\ &137\ \\ &195\ &203\ &270\ &216\ &155\ &277\ &202\ &151\ \\ &158\ &272\ &276\ &284\ &156\ &278\ &215\ &149\ \\ &201\ &255\ &285\ &251\ &160\ &299\ &207\ &192\ \\ &130\ &189\ &216\ &238\ &172\ &236\ &171\ &157\ \end{pmatrix}\end{aligned}$$
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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.