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$$\large{\displaylines{\normalsize \begin{array}{l|l} 1 & \large\underbrace{\mathbf{A}}_{m\times\color{#ff7800}n}\times\underbrace{\mathbf{v}}_{{\color{#ff7800}n}\times 1}=\underbrace{\mathbf{w}}_{m\times 1}\\ \\ & {\color{#ff7800}\begin{pmatrix}1&2\\3&4\\5&6\end{pmatrix}}\begin{pmatrix}1\\2\end{pmatrix}=\begin{pmatrix}{\color{#ff7800}1}\cdot1+{\color{#ff7800}2}\cdot2\\{\color{#ff7800}3}\cdot1+{\color{#ff7800}4}\cdot2\\{\color{#ff7800}5}\cdot1+{\color{#ff7800}6}\cdot2\end{pmatrix}\\ \\ 2 & \large\underbrace{\mathbf{v}^{T}}_{1\times\color{#ff7800}m}\times\underbrace{\mathbf{A}}_{{\color{#ff7800}m}\times n}=\underbrace{\mathbf{w}^{T}}_{1\times n}\\ \\ & \begin{pmatrix}1&2\end{pmatrix}{\color{#ff7800}\begin{pmatrix}1&2\\3&4\end{pmatrix}}=\\ & =\begin{pmatrix}1\cdot{\color{#ff7800}1}+2\cdot{\color{#ff7800}3}&1\cdot{\color{#ff7800}2}+2\cdot{\color{#ff7800}4}\end{pmatrix} \end{array}}}$$

. . . операции над матрицами умножение матриц