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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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &2\ &3\ &5\ &6\ \\ &4\ &5\ &6\ &3\ \\ &3\ &2\ &0\ &4\ \\ &8\ &8\ &5\ &6\ \end{pmatrix}\times \begin{pmatrix} &3\ &5\ &9\ &1\ \\ &3\ &5\ &2\ &4\ \\ &9\ &6\ &2\ &4\ \\ &0\ &2\ &5\ &7\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &2\ &3\ &4\ \\ &3\ &8\ &6\ &7\ &9\ \\ &2\ &6\ &5\ &7\ &8\ \\ &3\ &7\ &7\ &8\ &10\ \\ &4\ &9\ &8\ &10\ &17\ \end{pmatrix}\times \begin{pmatrix} &42\ &-9\ &-19\ &15\ &-5\ \\ &-9\ &3\ &4\ &-4\ &1\ \\ &-19\ &4\ &7\ &-5\ &2\ \\ &15\ &-4\ &-5\ &5\ &-2\ \\ &-5\ &1\ &2\ &-2\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &-8\ &0\ &0\ \\ &0\ &-27\ &27\ \\ &0\ &0\ &-27\ \end{pmatrix}\times \begin{pmatrix} &-2\ &0\ &0\ \\ &0\ &-3\ &1\ \\ &0\ &0\ &-3\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &0\ &1\ \\ &-1\ &0\ \end{pmatrix}\times \begin{pmatrix} &0\ &1\ \\ &-1\ &0\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &0\ &0\ &1\ \\ &0\ &0\ &0\ \\ &1\ &1\ &0\ \end{pmatrix}\times \begin{pmatrix} &0\ &0\ &0\ \\ &0\ &0\ &0\ \\ &0\ &0\ &0\ \end{pmatrix}}\\ \end{aligned}$$
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$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &2\ &3\ &4\ \\ &3\ &8\ &6\ &7\ &9\ \\ &2\ &6\ &5\ &7\ &8\ \\ &3\ &7\ &7\ &8\ &10\ \\ &4\ &9\ &8\ &10\ &17\ \end{pmatrix}\times \begin{pmatrix} &42\ &-9\ &-19\ &15\ &-5\ \\ &-9\ &3\ &4\ &-4\ &1\ \\ &-19\ &4\ &7\ &-5\ &2\ \\ &15\ &-4\ &-5\ &5\ &-2\ \\ &-5\ &1\ &2\ &-2\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &-8\ &0\ &0\ \\ &0\ &-27\ &27\ \\ &0\ &0\ &-27\ \end{pmatrix}\times \begin{pmatrix} &-2\ &0\ &0\ \\ &0\ &-3\ &1\ \\ &0\ &0\ &-3\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &0\ &1\ \\ &-1\ &0\ \end{pmatrix}\times \begin{pmatrix} &0\ &1\ \\ &-1\ &0\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &0\ &0\ &1\ \\ &0\ &0\ &0\ \\ &1\ &1\ &0\ \end{pmatrix}\times \begin{pmatrix} &0\ &0\ &0\ \\ &0\ &0\ &0\ \\ &0\ &0\ &0\ \end{pmatrix}}\\ \end{aligned}$$
First page << Page25 Page26 Page27 Page28 ... ... Page42 Page43 Page44 >> Last page 共48页
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.