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polimi-cheatsheet
GitHub Repository: polimi-cheatsheet/GAL-cheatsheet
 Path: blob/master/esercizi/1.risoluzione-sistemi.tex
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\subsection{Risoluzione di sistemi}

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\begin{tabular}{ll}

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	\(

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		\begin{cases}

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			2x+4y+4z=4 \\[-0.3em]

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			x-z=1 \\[-0.3em]

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			-x+3y+4z=2 \\

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		\end{cases}

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	\)

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	&

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	\(

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	A|\vec{b} = \left[

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	\arraycolsep=2.5pt\def\arraystretch{1.2}

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	\begin{array}{@{}ccc|c}

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		2 & 4 & 4 & 4 \\[-0.3em]

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		1 & 0 & -1 & 1 \\[-0.3em]

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		-1 & 3 & 4 & 2 \\

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	\end{array}

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	\right]

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	\)

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\end{tabular}

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Riducendo $A|\vec{b}$ a scala

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\(

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\left[

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	\arraycolsep=2.5pt\def\arraystretch{1.2}

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	\begin{array}{@{}ccc|c}

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		2 & 4 & 4 & 4 \\[-0.3em]

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		1 & 0 & -1 & 1 \\[-0.3em]

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		-1 & 3 & 4 & 2 \\

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	\end{array}

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\right]

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\rightarrow

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\left[

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	\arraycolsep=2.5pt\def\arraystretch{1.2}

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	\begin{array}{@{}ccc|c}

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		1 & 0 & -1 & 1 \\[-0.3em]

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		1 & 2 & 2 & 2 \\[-0.3em]

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		-1 & 3 & 4 & 2 \\

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	\end{array}

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\right]

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\rightarrow

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\left[

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	\arraycolsep=2.5pt\def\arraystretch{1.2}

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	\begin{array}{@{}ccc|c}

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		1 & 0 & -1 & 1 \\[-0.3em]

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		0 & 2 & 3 & 1 \\[-0.3em]

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		0 & 3 & 3 & 3 \\

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	\end{array}

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\right]

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\rightarrow

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\left[

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	\arraycolsep=2.5pt\def\arraystretch{1.2}

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	\begin{array}{@{}ccc|c}

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		1 & 0 & -1 & 1 \\[-0.3em]

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		0 & 2 & 3 & 1 \\[-0.3em]

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		0 & 1 & 1 & 1 \\

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	\end{array}

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\right]

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\rightarrow

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\left[

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	\arraycolsep=2.5pt\def\arraystretch{1.2}

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	\begin{array}{@{}ccc|c}

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		\circled{1} & 0 & -1 & 1 \\[-0.3em]

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		0 & \circled{2} & 3 & 1 \\[-0.3em]

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		0 & 0 & \circled{1} & -1 \\

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	\end{array}

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\right]

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\rightarrow

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\begin{cases}

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	x - z = 1 \\[-0.3em]

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	2y + 3z = 1 \\[-0.3em]

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	z = -1 \\

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\end{cases}

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\)

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