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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} &3\ &4\ \\ &2\ &7\ \\ &9\ &1\ \end{pmatrix}\times \begin{pmatrix} &6\ &\frac{13}{2}\ &3\ \\ &3\ &5\ &5\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &5\ &7\ &6\ &8\ \end{pmatrix}\times \begin{pmatrix} &3\ \\ &5\ \\ &7\ \\ &6\ \\ &8\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &2\ &8\ &5\ &7\ &4\ \\ &3\ &6\ &1\ &10\ &9\ \end{pmatrix}\times \begin{pmatrix} &2\ &8\ \\ &5\ &7\ \\ &4\ &3\ \\ &6\ &1\ \\ &10\ &9\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ &3\ \\ &4\ &5\ &6\ \\ &7\ &8\ &9\ \end{pmatrix}\times \begin{pmatrix} &9\ &8\ &7\ \\ &6\ &5\ &4\ \\ &3\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &-\frac{5}{3}\ &\frac{2}{3}\ \\ &\frac{1}{3}\ &2\ \end{pmatrix}\times \begin{pmatrix} &\frac{3}{4}\ &-\frac{5}{4}\ \\ &\frac{1}{2}\ &0\ \end{pmatrix}}\\ \end{aligned}
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\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &5\ &7\ &6\ &8\ \end{pmatrix}\times \begin{pmatrix} &3\ \\ &5\ \\ &7\ \\ &6\ \\ &8\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &2\ &8\ &5\ &7\ &4\ \\ &3\ &6\ &1\ &10\ &9\ \end{pmatrix}\times \begin{pmatrix} &2\ &8\ \\ &5\ &7\ \\ &4\ &3\ \\ &6\ &1\ \\ &10\ &9\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ &3\ \\ &4\ &5\ &6\ \\ &7\ &8\ &9\ \end{pmatrix}\times \begin{pmatrix} &9\ &8\ &7\ \\ &6\ &5\ &4\ \\ &3\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &-\frac{5}{3}\ &\frac{2}{3}\ \\ &\frac{1}{3}\ &2\ \end{pmatrix}\times \begin{pmatrix} &\frac{3}{4}\ &-\frac{5}{4}\ \\ &\frac{1}{2}\ &0\ \end{pmatrix}}\\ \end{aligned}
First page << Page28 Page29 Page30 Page31 ... ... Page45 Page46 Page47 >> 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.