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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &-\frac{1}{2}\ &0\ &\frac{3}{2}\ \\ &-\frac{3}{2}\ &-1\ &\frac{3}{2}\ \\ &-\frac{1}{2}\ &0\ &-\frac{1}{2}\ \end{pmatrix}\times \begin{pmatrix} &-\frac{1}{2}\ &0\ &-\frac{3}{2}\ \\ &\frac{3}{2}\ &-1\ &\frac{3}{2}\ \\ &\frac{1}{2}\ &0\ &-\frac{1}{2}\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &65\ &2\ \\ &4\ &84\ &3\ \\ &34\ &7\ &89\ \end{pmatrix}\times \begin{pmatrix} &-\frac{7455}{14711}\ &\frac{5771}{14711}\ &-\frac{27}{14711}\ \\ &\frac{254}{14711}\ &-\frac{21}{14711}\ &-\frac{5}{14711}\ \\ &\frac{2828}{14711}\ &-\frac{2203}{14711}\ &\frac{176}{14711}\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &0\ \\ &0\ &2\ &1\ \\ &-1\ &0\ &1\ \end{pmatrix}\times \begin{pmatrix} &-2\ &3\ &-3\ \\ &1\ &-1\ &1\ \\ &-2\ &3\ &-2\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &2\ \end{pmatrix}\times \begin{pmatrix} &3\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &34\ &8\ &4\ &8\ \\ &9\ &30\ &84\ &2\ \\ &94\ &9\ &39\ &3\ \end{pmatrix}\times \begin{pmatrix} &23\ &8\ &3\ &3\ &9\ \\ &3\ &3\ &7\ &56\ &7\ \\ &9\ &3\ &9\ &5\ &2\ \\ &9\ &2\ &1\ &4\ &5\ \end{pmatrix}}\\ \end{aligned}$$
First page << Page28 Page29 Page30 Page31 ... ... Page35 Page36 Page37 >> Last page 共37页
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &65\ &2\ \\ &4\ &84\ &3\ \\ &34\ &7\ &89\ \end{pmatrix}\times \begin{pmatrix} &-\frac{7455}{14711}\ &\frac{5771}{14711}\ &-\frac{27}{14711}\ \\ &\frac{254}{14711}\ &-\frac{21}{14711}\ &-\frac{5}{14711}\ \\ &\frac{2828}{14711}\ &-\frac{2203}{14711}\ &\frac{176}{14711}\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &0\ \\ &0\ &2\ &1\ \\ &-1\ &0\ &1\ \end{pmatrix}\times \begin{pmatrix} &-2\ &3\ &-3\ \\ &1\ &-1\ &1\ \\ &-2\ &3\ &-2\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &2\ \end{pmatrix}\times \begin{pmatrix} &3\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &34\ &8\ &4\ &8\ \\ &9\ &30\ &84\ &2\ \\ &94\ &9\ &39\ &3\ \end{pmatrix}\times \begin{pmatrix} &23\ &8\ &3\ &3\ &9\ \\ &3\ &3\ &7\ &56\ &7\ \\ &9\ &3\ &9\ &5\ &2\ \\ &9\ &2\ &1\ &4\ &5\ \end{pmatrix}}\\ \end{aligned}$$
First page << Page28 Page29 Page30 Page31 ... ... Page35 Page36 Page37 >> Last page 共37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.