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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{853}{500}\ &\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{337}{1000}\ &-\frac{9}{200}\ &\frac{457}{1000}\ &\frac{273}{1000}\ &-\frac{9}{125}\ \\ &-\frac{34}{125}\ &-\frac{213}{500}\ &-\frac{24}{125}\ &-\frac{17}{200}\ &\frac{61}{250}\ \\ &-\frac{163}{1000}\ &-\frac{9}{250}\ &-\frac{409}{1000}\ &-\frac{457}{1000}\ &\frac{3}{40}\ \\ &-\frac{62}{125}\ &\frac{723}{1000}\ &-\frac{31}{125}\ &\frac{169}{500}\ &\frac{2}{25}\ \\ &\frac{21}{200}\ &\frac{7}{100}\ &-\frac{97}{1000}\ &-\frac{129}{250}\ &\frac{46}{125}\ \end{pmatrix}}\\ \\Solution:&\\&\begin{pmatrix} &\frac{853}{500}\ &\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{337}{1000}\ &-\frac{9}{200}\ &\frac{457}{1000}\ &\frac{273}{1000}\ &-\frac{9}{125}\ \\ &-\frac{34}{125}\ &-\frac{213}{500}\ &-\frac{24}{125}\ &-\frac{17}{200}\ &\frac{61}{250}\ \\ &-\frac{163}{1000}\ &-\frac{9}{250}\ &-\frac{409}{1000}\ &-\frac{457}{1000}\ &\frac{3}{40}\ \\ &-\frac{62}{125}\ &\frac{723}{1000}\ &-\frac{31}{125}\ &\frac{169}{500}\ &\frac{2}{25}\ \\ &\frac{21}{200}\ &\frac{7}{100}\ &-\frac{97}{1000}\ &-\frac{129}{250}\ &\frac{46}{125}\ \end{pmatrix}\\\\=\ \ &\begin{pmatrix} &\frac{242127}{200000}\ &-\frac{1696519}{1000000}\ &\frac{596017}{1000000}\ &-\frac{1368221}{1000000}\ &\frac{359447}{500000}\ \\ &\frac{12839}{100000}\ &\frac{67487}{125000}\ &\frac{36479}{100000}\ &\frac{823393}{1000000}\ &-\frac{66691}{100000}\ \\ &-\frac{703067}{1000000}\ &\frac{27567}{200000}\ &-\frac{108967}{200000}\ &-\frac{14709}{500000}\ &\frac{339651}{1000000}\ \\ &\frac{125389}{500000}\ &\frac{103033}{250000}\ &\frac{17173}{62500}\ &\frac{312271}{1000000}\ &-\frac{179951}{500000}\ \\ &-\frac{168497}{250000}\ &\frac{577617}{1000000}\ &-\frac{25193}{62500}\ &\frac{216327}{500000}\ &-\frac{7673}{100000}\ \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.