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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
$$ \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &43\ &26\ &32\ \\ &74\ &37\ &59\ &86\ \\ &24\ &56\ &85\ &37\ \\ &96\ &45\ &28\ &43\ \end{pmatrix}\times \begin{pmatrix} &-\frac{23506}{1943373}\ &-\frac{7025}{3886746}\ &\frac{4331}{3886746}\ &\frac{15103}{1295582}\ \\ &\frac{16749}{647791}\ &-\frac{19053}{1295582}\ &-\frac{1901}{1295582}\ &\frac{14813}{1295582}\ \\ &-\frac{110617}{5830119}\ &\frac{28369}{11660238}\ &\frac{208799}{11660238}\ &-\frac{23921}{3886746}\ \\ &\frac{71713}{5830119}\ &\frac{208031}{11660238}\ &-\frac{147065}{11660238}\ &-\frac{41695}{3886746}\ \end{pmatrix}}\\ \\Solution:&\\&\begin{pmatrix} &1\ &43\ &26\ &32\ \\ &74\ &37\ &59\ &86\ \\ &24\ &56\ &85\ &37\ \\ &96\ &45\ &28\ &43\ \end{pmatrix}\times \begin{pmatrix} &-\frac{23506}{1943373}\ &-\frac{7025}{3886746}\ &\frac{4331}{3886746}\ &\frac{15103}{1295582}\ \\ &\frac{16749}{647791}\ &-\frac{19053}{1295582}\ &-\frac{1901}{1295582}\ &\frac{14813}{1295582}\ \\ &-\frac{110617}{5830119}\ &\frac{28369}{11660238}\ &\frac{208799}{11660238}\ &-\frac{23921}{3886746}\ \\ &\frac{71713}{5830119}\ &\frac{208031}{11660238}\ &-\frac{147065}{11660238}\ &-\frac{41695}{3886746}\ \end{pmatrix}\\\\=\ \ &\begin{pmatrix} &\frac{1163}{1163}\ &0\ &0\ &0\ \\ &0\ &\frac{1163}{1163}\ &0\ &0\ \\ &0\ &0\ &\frac{1163}{1163}\ &0\ \\ &0\ &0\ &0\ &\frac{1163}{1163}\ \end{pmatrix}\end{aligned}$$
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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.