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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} &21\ &34\ &20\ \\ &5\ &78\ &20\ \\ &21\ &14\ &17\ \\ &34\ &31\ &38\ \end{pmatrix}\times \begin{pmatrix} &\frac{7667}{10000}\ \\ &\frac{11867}{10000}\ \\ &\frac{8767}{10000}\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ &0\ \\ &2\ &5\ &-1\ \\ &4\ &10\ &-1\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ &4\ \\ &2\ &5\ &10\ \\ &0\ &-1\ &-1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &2\ &4\ &1\ \\ &8\ &9\ &0\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ \\ &3\ &5\ \\ &2\ &6\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ \\ &3\ &5\ \\ &2\ &6\ \end{pmatrix}\times \begin{pmatrix} &2\ &4\ &1\ \\ &8\ &9\ &0\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &4\ \\ &2\ &6\ &5\ \\ &3\ &2\ &4\ \end{pmatrix}\times \begin{pmatrix} &2\ &3\ &1\ \\ &4\ &1\ &2\ \\ &4\ &5\ &3\ \end{pmatrix}}\\ \end{aligned}
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\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ &0\ \\ &2\ &5\ &-1\ \\ &4\ &10\ &-1\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ &4\ \\ &2\ &5\ &10\ \\ &0\ &-1\ &-1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &2\ &4\ &1\ \\ &8\ &9\ &0\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ \\ &3\ &5\ \\ &2\ &6\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ \\ &3\ &5\ \\ &2\ &6\ \end{pmatrix}\times \begin{pmatrix} &2\ &4\ &1\ \\ &8\ &9\ &0\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &4\ \\ &2\ &6\ &5\ \\ &3\ &2\ &4\ \end{pmatrix}\times \begin{pmatrix} &2\ &3\ &1\ \\ &4\ &1\ &2\ \\ &4\ &5\ &3\ \end{pmatrix}}\\ \end{aligned}
First page << Page15 Page16 Page17 Page18 ... ... Page32 Page33 Page34 >> 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.