Example

Denote numpy.add by \(\stackrel{?}{+}\) and let

\[\begin{align*}
  A = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix}, \quad
  \vec{v} = \begin{pmatrix} 1 \\ 2 \end{pmatrix};
\end{align*}
\]

then

\[\begin{align*}
  A \stackrel{?}{+} \vec{v}
  & = A + 1 \vec{v}^{\mathsf{T}} \\
  & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix}
    + \vec{1} {\begin{pmatrix} 1 \\ 2 \end{pmatrix}}^{\!\!\mathsf{T}} \\
  & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix}
    + \begin{pmatrix} 1 \\ 1 \end{pmatrix}
      \begin{pmatrix} 1 & 2 \end{pmatrix} \\
  & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix}
    + \begin{pmatrix} 1 \\ 1 \end{pmatrix}
      \begin{pmatrix} 1 & 2 \end{pmatrix} \\
  & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix}
    + \begin{pmatrix} 1 & 2 \\ 1 & 2 \end{pmatrix} \\
  & = \begin{pmatrix} 101 & 202 \\ 301 & 402 \end{pmatrix}
\end{align*}
\]

and

import numpy as np
a = np.array([[100, 200], [300, 400]])
v = np.array([1, 2])
a + v

array([[101, 202],
       [301, 402]])