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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} &\frac{269}{250}\ &\frac{231}{200}\ &\frac{259}{500}\ &-\frac{1707}{1000}\ &\frac{1787}{1000}\ \\ &-\frac{19}{100}\ &-\frac{1133}{1000}\ &-\frac{207}{500}\ &\frac{37}{250}\ &-\frac{523}{500}\ \\ &-\frac{133}{200}\ &\frac{207}{250}\ &-\frac{207}{1000}\ &\frac{153}{250}\ &\frac{153}{1000}\ \\ &-\frac{1403}{1000}\ &-\frac{621}{500}\ &-\frac{29}{20}\ &-\frac{63}{200}\ &-\frac{13}{200}\ \\ &\frac{591}{500}\ &\frac{49}{125}\ &\frac{777}{500}\ &\frac{1261}{1000}\ &-\frac{207}{250}\ \end{pmatrix}\times \begin{pmatrix} &-\frac{83}{1000}\ &-\frac{333}{1000}\ &\frac{74}{125}\ &-\frac{93}{250}\ &\frac{373}{200}\ \\ &-\frac{247}{500}\ &-\frac{87}{250}\ &\frac{319}{500}\ &-\frac{457}{1000}\ &-\frac{447}{1000}\ \\ &-\frac{509}{1000}\ &-\frac{573}{1000}\ &\frac{53}{500}\ &\frac{248}{125}\ &-\frac{39}{125}\ \\ &-\frac{427}{500}\ &\frac{1979}{1000}\ &\frac{5}{8}\ &-\frac{423}{1000}\ &\frac{1}{1000}\ \\ &\frac{97}{50}\ &-\frac{181}{250}\ &-\frac{49}{25}\ &-\frac{733}{1000}\ &-\frac{1107}{1000}\ \end{pmatrix}}\\ \\Solution:&\\&\begin{pmatrix} &\frac{269}{250}\ &\frac{231}{200}\ &\frac{259}{500}\ &-\frac{1707}{1000}\ &\frac{1787}{1000}\ \\ &-\frac{19}{100}\ &-\frac{1133}{1000}\ &-\frac{207}{500}\ &\frac{37}{250}\ &-\frac{523}{500}\ \\ &-\frac{133}{200}\ &\frac{207}{250}\ &-\frac{207}{1000}\ &\frac{153}{250}\ &\frac{153}{1000}\ \\ &-\frac{1403}{1000}\ &-\frac{621}{500}\ &-\frac{29}{20}\ &-\frac{63}{200}\ &-\frac{13}{200}\ \\ &\frac{591}{500}\ &\frac{49}{125}\ &\frac{777}{500}\ &\frac{1261}{1000}\ &-\frac{207}{250}\ \end{pmatrix}\times \begin{pmatrix} &-\frac{83}{1000}\ &-\frac{333}{1000}\ &\frac{74}{125}\ &-\frac{93}{250}\ &\frac{373}{200}\ \\ &-\frac{247}{500}\ &-\frac{87}{250}\ &\frac{319}{500}\ &-\frac{457}{1000}\ &-\frac{447}{1000}\ \\ &-\frac{509}{1000}\ &-\frac{573}{1000}\ &\frac{53}{500}\ &\frac{248}{125}\ &-\frac{39}{125}\ \\ &-\frac{427}{500}\ &\frac{1979}{1000}\ &\frac{5}{8}\ &-\frac{423}{1000}\ &\frac{1}{1000}\ \\ &\frac{97}{50}\ &-\frac{181}{250}\ &-\frac{49}{25}\ &-\frac{733}{1000}\ &-\frac{1107}{1000}\ \end{pmatrix}\\\\=\ \ &\begin{pmatrix} &\frac{2000509}{500000}\ &-\frac{5729003}{1000000}\ &-\frac{628121}{200000}\ &-\frac{97641}{200000}\ &-\frac{651077}{1000000}\ \\ &-\frac{684717}{500000}\ &\frac{436243}{250000}\ &\frac{631721}{500000}\ &\frac{471199}{1000000}\ &\frac{1439339}{1000000}\ \\ &-\frac{237151}{500000}\ &\frac{36009}{31250}\ &\frac{97631}{500000}\ &-\frac{912729}{1000000}\ &-\frac{428629}{250000}\ \\ &\frac{1610957}{1000000}\ &\frac{57697}{50000}\ &-\frac{1846147}{1000000}\ &-\frac{1004}{625}\ &-\frac{1537381}{1000000}\ \\ &-\frac{1882977}{500000}\ &\frac{1674527}{1000000}\ &\frac{3525569}{1000000}\ &\frac{2537809}{1000000}\ &\frac{492443}{200000}\ \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.