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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} &1\ &2\ \end{pmatrix}\times \begin{pmatrix} &3\ \\ &4\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ &3\ \\ &4\ &5\ &6\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ \\ &3\ &4\ \\ &5\ &6\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &7\ &105\ &2275\ \\ &105\ &2275\ &55125\ \\ &2275\ &55125\ &1421875\ \end{pmatrix}\times \begin{pmatrix} &0\ \\ &0\ \\ &0\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ \\ &6\ \\ &4\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ &2\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &4\ &5\ &6\ &7\ &8\ &9\ &5\ &4\ &1\ \end{pmatrix}\times \begin{pmatrix} &7\ \\ &8\ \\ &5\ \\ &4\ \\ &9\ \\ &6\ \\ &3\ \\ &1\ \\ &5\ \end{pmatrix}}\\ \end{aligned}
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\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ &3\ \\ &4\ &5\ &6\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ \\ &3\ &4\ \\ &5\ &6\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &7\ &105\ &2275\ \\ &105\ &2275\ &55125\ \\ &2275\ &55125\ &1421875\ \end{pmatrix}\times \begin{pmatrix} &0\ \\ &0\ \\ &0\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ \\ &6\ \\ &4\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ &2\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &4\ &5\ &6\ &7\ &8\ &9\ &5\ &4\ &1\ \end{pmatrix}\times \begin{pmatrix} &7\ \\ &8\ \\ &5\ \\ &4\ \\ &9\ \\ &6\ \\ &3\ \\ &1\ \\ &5\ \end{pmatrix}}\\ \end{aligned}
First page << Page49 Page50 Page51 Last page 共51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.