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Mathematics
         
语言:中文    Language:English
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.
    Current location:Linear algebra >Matrix multiplication >History of matrix multiplication
     \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &1\ &1\ &1\ \\ &2\ &2\ &2\ \\ &3\ &3\ &3\ \end{pmatrix}\times \begin{pmatrix} &1\ &2\ &3\ \\ &1\ &2\ &3\ \\ &1\ &2\ &3\ \end{pmatrix}}\\ \end{aligned}
     \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &3\ &1\ &4\ \\ &-2\ &0\ &1\ \\ &1\ &2\ &2\ \end{pmatrix}\times \begin{pmatrix} &1\ &-3\ &2\ \\ &0\ &1\ &-4\ \\ &2\ &1\ &1\ \end{pmatrix}}\\ \end{aligned}
     \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &345\ \end{pmatrix}\times \begin{pmatrix} &969\ \end{pmatrix}}\\ \end{aligned}
     \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &0\ \end{pmatrix}\times \begin{pmatrix} &0\ \end{pmatrix}}\\ \end{aligned}
     \begin{aligned}&\\ \color{black}{Calculate }& \color{black}{\ \ \begin{pmatrix} &123\ &234\ &345\ \\ &456\ &567\ &678\ \\ &789\ &890\ &901\ \end{pmatrix}\times \begin{pmatrix} &111\ &222\ &333\ \\ &444\ &555\ &666\ \\ &777\ &888\ &999\ \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.



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