\[ \vec{a} \perp \vec{b} \Leftrightarrow \vec{a} \cdot \vec{b} = 0 \]

\[ (A | \vec{b} ) \Leftrightarrow (I | \vec{x} ) \]

\[ (A | I ) \Leftrightarrow (I | A^{-1} ) \]

\[ \det(A \cdot B) = \det(A) \cdot \det(B) \]

\[ A \vec{x} = \lambda \vec{x}, \quad \vec{x} \neq \vec{0} \]

\[ \]