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Levi Pearson 2014-01-25 19:55:27 -07:00 committed by Gitit Wiki User
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commit f3903cd4ec
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@ -77,4 +77,38 @@ v_1\\ \vdots \\ v_n
\end{matrix}\right) = \left(\begin{matrix} \end{matrix}\right) = \left(\begin{matrix}
rv_1 \\ \vdots \\ rv_n rv_1 \\ \vdots \\ rv_n
\end{matrix}\right) \end{matrix}\right)
$$
This system:
$$\begin{alignedat}{4}
x & {}-{} & y & {}+{} & z & = 1\\
3x & {}+{} & & & z & = 3\\
5x & {}-{} & 2y & {}+{} & 3z & = 5
\end{alignedat}$$
reduces
$$
\left(\begin{array}{rrr|r}
1&-1&1&1\\
3&0&1&3\\
5&-2&3&5\\
\end{array}\right) \longrightarrow_{-5\rho_1+\rho_3}^{-3\rho_1+\rho_2}
\left(\begin{array}{rrr|r}
1&-1&1&1\\
0&3&-2&0\\
0&3&-2&0\\
\end{array}\right) \longrightarrow^{-\rho_2+\rho_3}
\left(\begin{array}{rrr|r}
1&-1&1&1\\
0&3&-2&0\\
0&0&0&0\\
\end{array}\right)
$$
to a one parameter solution set:
$$
\{ \begin{pmatrix}1\\ 0\\ 0\end{pmatrix} +
\begin{pmatrix}-1/3\\ 2/3\\ 1\end{pmatrix} z \mid z \in \Bbb{R} \}
$$ $$