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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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &2\ &1\ \\ &-2\ &1\ &2\ \\ &1\ &3\ &2\ \end{pmatrix}\times \begin{pmatrix} &3\ &2\ &1\ \\ &-2\ &1\ &2\ \\ &1\ &3\ &2\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &2\ &1\ \\ &-2\ &1\ &2\ \\ &1\ &3\ &2\ \end{pmatrix}\times \begin{pmatrix} &1\ &-1\ &0\ \\ &2\ &-2\ &5\ \\ &3\ &4\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &\frac{3}{2}\ &\frac{3}{4}\ \\ &6\ &3\ &\frac{3}{2}\ \\ &12\ &6\ &3\ \end{pmatrix}\times \begin{pmatrix} &1\ &\frac{1}{2}\ &\frac{1}{4}\ \\ &2\ &1\ &\frac{1}{2}\ \\ &4\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &\frac{1}{2}\ &\frac{1}{4}\ \\ &2\ &1\ &\frac{1}{2}\ \\ &4\ &2\ &1\ \end{pmatrix}\times \begin{pmatrix} &1\ &\frac{1}{2}\ &\frac{1}{4}\ \\ &2\ &1\ &\frac{1}{2}\ \\ &4\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &1\ &1\ \\ &2\ &2\ &2\ \\ &3\ &3\ &3\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ &3\ \\ &1\ &2\ &3\ \\ &1\ &2\ &3\ \end{pmatrix}}\\ \end{aligned}$$
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$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &2\ &1\ \\ &-2\ &1\ &2\ \\ &1\ &3\ &2\ \end{pmatrix}\times \begin{pmatrix} &1\ &-1\ &0\ \\ &2\ &-2\ &5\ \\ &3\ &4\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &\frac{3}{2}\ &\frac{3}{4}\ \\ &6\ &3\ &\frac{3}{2}\ \\ &12\ &6\ &3\ \end{pmatrix}\times \begin{pmatrix} &1\ &\frac{1}{2}\ &\frac{1}{4}\ \\ &2\ &1\ &\frac{1}{2}\ \\ &4\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &\frac{1}{2}\ &\frac{1}{4}\ \\ &2\ &1\ &\frac{1}{2}\ \\ &4\ &2\ &1\ \end{pmatrix}\times \begin{pmatrix} &1\ &\frac{1}{2}\ &\frac{1}{4}\ \\ &2\ &1\ &\frac{1}{2}\ \\ &4\ &2\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &1\ &1\ \\ &2\ &2\ &2\ \\ &3\ &3\ &3\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ &3\ \\ &1\ &2\ &3\ \\ &1\ &2\ &3\ \end{pmatrix}}\\ \end{aligned}$$
First page << Page30 Page31 Page32 Page33 ... ... Page46 Page47 Page48 >> Last page 共48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.