1.matrice-inversa.tex

\subsection{Trovare l'inversa di una matrice}
\(
A|I_2 = \left[
	\arraycolsep=2.0pt\def\arraystretch{1.0}
	\begin{array}{cc|cc}
		1 & 2 & 1 & 0 \\
		2 & -1 & 0 & 1 \\
	\end{array}
\right]
\rightarrow
\left[
	\arraycolsep=2.0pt\def\arraystretch{1.0}
	\begin{array}{cc|cc}
		1 & 2 & 1 & 0 \\
		0 & 5 & 2 & -1 \\
	\end{array}
\right]
\rightarrow
\left[
	\arraycolsep=2.0pt\def\arraystretch{1.0}
	\begin{array}{cc|cc}
		1 & 2 & 1 & 0 \\
		0 & 1 & 2/5 & -1/5 \\
	\end{array}
\right]
\rightarrow
\left[
	\arraycolsep=2.0pt\def\arraystretch{1.0}
	\begin{array}{cc|cc}
		1 & 0 & 1/5 & 2/5 \\
		0 & 1 & 2/5 & -1/5 \\
	\end{array}
\right]
\rightarrow
A^{-1} =
\frac{1}{5}
\left[
	\arraycolsep=2.0pt\def\arraystretch{1.0}
	\begin{array}{cc}
		1 & 2 \\
		2 & -1 \\
	\end{array}
\right]
\)