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Matrix equation

A linear system written as a matrix multiplication,

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

• Synonyms
• Equivalence: Vector equation
• Equivalence: Augmented matrix
• Solutions and invertibility
• Example: Homogeneous consistent system
• Example: Non-homogeneous consistent system
• Example: Non-homogeneous inconsistent system