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Equivalence: Vector equation

The matrix equation

\[\begin{equation*}
  A \vec{x} = \vec{b}
\end{equation*}
\]

is equivalent to the vector equation

\[\begin{equation*}
  x_1 \vec{a}_1 + \cdots + x_n \vec{a}_n = \vec{b}.
\end{equation*}
\]