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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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &111111\ \end{pmatrix}\times \begin{pmatrix} &111111\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1321\ \end{pmatrix}\times \begin{pmatrix} &2244\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &12\ \end{pmatrix}\times \begin{pmatrix} &34\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &5\ &7\ &9\ &11\ &13\ &15\ &17\ &19\ \\ &121\ &23\ &25\ &27\ &29\ &31\ &33\ &35\ &37\ &39\ \\ &441\ &43\ &45\ &47\ &49\ &51\ &53\ &55\ &57\ &59\ \\ &961\ &63\ &65\ &67\ &69\ &71\ &73\ &75\ &77\ &79\ \\ &1681\ &83\ &85\ &87\ &89\ &91\ &93\ &95\ &97\ &99\ \\ &2601\ &103\ &105\ &107\ &109\ &111\ &113\ &115\ &117\ &119\ \\ &3721\ &123\ &125\ &127\ &129\ &131\ &133\ &135\ &137\ &139\ \\ &5041\ &143\ &145\ &147\ &149\ &151\ &153\ &155\ &157\ &159\ \\ &6561\ &163\ &165\ &167\ &169\ &171\ &173\ &175\ &177\ &179\ \\ &8281\ &183\ &185\ &187\ &189\ &191\ &193\ &195\ &197\ &199\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \end{pmatrix}\times \begin{pmatrix} &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ \end{pmatrix}}\\ \end{aligned}$$
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$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1321\ \end{pmatrix}\times \begin{pmatrix} &2244\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &12\ \end{pmatrix}\times \begin{pmatrix} &34\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &3\ &5\ &7\ &9\ &11\ &13\ &15\ &17\ &19\ \\ &121\ &23\ &25\ &27\ &29\ &31\ &33\ &35\ &37\ &39\ \\ &441\ &43\ &45\ &47\ &49\ &51\ &53\ &55\ &57\ &59\ \\ &961\ &63\ &65\ &67\ &69\ &71\ &73\ &75\ &77\ &79\ \\ &1681\ &83\ &85\ &87\ &89\ &91\ &93\ &95\ &97\ &99\ \\ &2601\ &103\ &105\ &107\ &109\ &111\ &113\ &115\ &117\ &119\ \\ &3721\ &123\ &125\ &127\ &129\ &131\ &133\ &135\ &137\ &139\ \\ &5041\ &143\ &145\ &147\ &149\ &151\ &153\ &155\ &157\ &159\ \\ &6561\ &163\ &165\ &167\ &169\ &171\ &173\ &175\ &177\ &179\ \\ &8281\ &183\ &185\ &187\ &189\ &191\ &193\ &195\ &197\ &199\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ &1\ \\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &1\ \end{pmatrix}}\\ \end{aligned}$$
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \\ &1\ \end{pmatrix}\times \begin{pmatrix} &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ &0\ \end{pmatrix}}\\ \end{aligned}$$
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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.