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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\ &3\ &4\ \\ &2\ &6\ &5\ \\ &3\ &2\ &4\ \end{pmatrix}\times \begin{pmatrix} &1\ &3\ &4\ \\ &2\ &6\ &5\ \\ &3\ &2\ &4\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &-1\ &3\ \\ &4\ &3\ &2\ \end{pmatrix}\times \begin{pmatrix} &-\frac{1}{3}\ &\frac{2}{3}\ &-\frac{1}{3}\ \\ &\frac{2}{3}\ &-\frac{1}{3}\ &\frac{2}{3}\ \\ &-1\ &1\ &0\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &10\ &-3\ &-8\ \\ &-6\ &2\ &5\ \\ &-3\ &1\ &2\ \end{pmatrix}\times \begin{pmatrix} &3\ &-1\ &-1\ \\ &4\ &-2\ &-1\ \\ &-3\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ \\ &1\ \\ &1\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &37\ &23\ &46\ &35\ \\ &52\ &36\ &39\ &89\ \\ &74\ &46\ &34\ &25\ \\ &47\ &47\ &82\ &59\ \end{pmatrix}\times \begin{pmatrix} &2\ &3\ &4\ &5\ \\ &6\ &2\ &7\ &3\ \\ &9\ &99\ &5\ &3\ \\ &1\ &2\ &9\ &83\ \end{pmatrix}}\\ \end{aligned}
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\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &-1\ &3\ \\ &4\ &3\ &2\ \end{pmatrix}\times \begin{pmatrix} &-\frac{1}{3}\ &\frac{2}{3}\ &-\frac{1}{3}\ \\ &\frac{2}{3}\ &-\frac{1}{3}\ &\frac{2}{3}\ \\ &-1\ &1\ &0\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &10\ &-3\ &-8\ \\ &-6\ &2\ &5\ \\ &-3\ &1\ &2\ \end{pmatrix}\times \begin{pmatrix} &3\ &-1\ &-1\ \\ &4\ &-2\ &-1\ \\ &-3\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ \\ &1\ \\ &1\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ \end{pmatrix}}\\ \end{aligned}
\begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &37\ &23\ &46\ &35\ \\ &52\ &36\ &39\ &89\ \\ &74\ &46\ &34\ &25\ \\ &47\ &47\ &82\ &59\ \end{pmatrix}\times \begin{pmatrix} &2\ &3\ &4\ &5\ \\ &6\ &2\ &7\ &3\ \\ &9\ &99\ &5\ &3\ \\ &1\ &2\ &9\ &83\ \end{pmatrix}}\\ \end{aligned}
First page << Page16 Page17 Page18 Page19 ... ... Page33 Page34 Page35 >> 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.