Equations
Unfold
Math OP
Unfold
Linear algebra
Fold
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} &\frac{2030}{60}\ \end{pmatrix}\times \begin{pmatrix} &\frac{40}{80}\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ \\ &3\ &4\ \end{pmatrix}\times \begin{pmatrix} &5\ &6\ \\ &7\ &8\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &8\ &-6\ &7\ \\ &-16\ &7\ &-13\ \\ &9\ &-3\ &7\ \end{pmatrix}\times \begin{pmatrix} &1\ &-18\ &15\ \\ &-1\ &-22\ &20\ \\ &1\ &-25\ &22\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &8\ &-16\ &9\ \\ &-6\ &7\ &-3\ \\ &7\ &-13\ &7\ \end{pmatrix}\times \begin{pmatrix} &1\ &-18\ &15\ \\ &-1\ &-22\ &20\ \\ &1\ &-25\ &22\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &-4\ &-2\ &5\ \\ &5\ &0\ &-5\ \\ &-3\ &1\ &5\ \end{pmatrix}\times \begin{pmatrix} &33\ &-17\ &-2\ \\ &-16\ &29\ &-16\ \\ &27\ &-15\ &-1\ \end{pmatrix}}\\ \end{aligned}
First page << Page17 Page18 Page19 Page20 ... ... Page34 Page35 Page36 >> Last page 共51页
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &2\ \\ &3\ &4\ \end{pmatrix}\times \begin{pmatrix} &5\ &6\ \\ &7\ &8\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &8\ &-6\ &7\ \\ &-16\ &7\ &-13\ \\ &9\ &-3\ &7\ \end{pmatrix}\times \begin{pmatrix} &1\ &-18\ &15\ \\ &-1\ &-22\ &20\ \\ &1\ &-25\ &22\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &8\ &-16\ &9\ \\ &-6\ &7\ &-3\ \\ &7\ &-13\ &7\ \end{pmatrix}\times \begin{pmatrix} &1\ &-18\ &15\ \\ &-1\ &-22\ &20\ \\ &1\ &-25\ &22\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &-4\ &-2\ &5\ \\ &5\ &0\ &-5\ \\ &-3\ &1\ &5\ \end{pmatrix}\times \begin{pmatrix} &33\ &-17\ &-2\ \\ &-16\ &29\ &-16\ \\ &27\ &-15\ &-1\ \end{pmatrix}}\\ \end{aligned}
First page << Page17 Page18 Page19 Page20 ... ... Page34 Page35 Page36 >> 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.