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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 >Answer
$$ \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}}\\ \\Solution:&\\&\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}\\\\=\ \ &\begin{pmatrix} &1\ &4\ &9\ &16\ &25\ &36\ &49\ &64\ &81\ &100\ \\ &121\ &144\ &169\ &196\ &225\ &256\ &289\ &324\ &361\ &400\ \\ &441\ &484\ &529\ &576\ &625\ &676\ &729\ &784\ &841\ &900\ \\ &961\ &1024\ &1089\ &1156\ &1225\ &1296\ &1369\ &1444\ &1521\ &1600\ \\ &1681\ &1764\ &1849\ &1936\ &2025\ &2116\ &2209\ &2304\ &2401\ &2500\ \\ &2601\ &2704\ &2809\ &2916\ &3025\ &3136\ &3249\ &3364\ &3481\ &3600\ \\ &3721\ &3844\ &3969\ &4096\ &4225\ &4356\ &4489\ &4624\ &4761\ &4900\ \\ &5041\ &5184\ &5329\ &5476\ &5625\ &5776\ &5929\ &6084\ &6241\ &6400\ \\ &6561\ &6724\ &6889\ &7056\ &7225\ &7396\ &7569\ &7744\ &7921\ &8100\ \\ &8281\ &8464\ &8649\ &8836\ &9025\ &9216\ &9409\ &9604\ &9801\ &10000\ \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.