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--- lecture_7a [2015/02/10 10:54] – [One more example] rupert
+++ lecture_7a [2015/02/10 10:55] (current) – [One more example] rupert
@@ Line 21: / Line 21: @@
 \go{1&0&-0.5&0}{0&1&1.5&2}{0&0&0&0}{0&0&0&0}
 \end{align*}
+Now $z$ is a free variable, say $z=t$ where $t\in \mathbb{R}$, and from row 2 we get $y=2-1.5t$ and row 1 gives $x=0.5t$, so the solution is
+\[ \begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}0\\2\\0\end{bmatrix}+t\begin{bmatrix}0.5\\-1.5\\1\end{bmatrix},\quad t\in\mathbb{R}.\]
 ===== Observations about Gaussian elimination =====