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lecture_4_slides
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| lecture_4_slides [2017/02/01 17:17] – [Reduced row echelon form (RREF)] rupert | lecture_4_slides [2017/02/01 17:19] (current) – [Example] rupert | ||
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| * $ x_1+2x_2+3x_3=8\implies x_1=5-2s-6t.$ | * $ x_1+2x_2+3x_3=8\implies x_1=5-2s-6t.$ | ||
| * So $ \left[\begin{smallmatrix} x_1\\x_2\\x_3\\x_4 \\x_5\end{smallmatrix}\right]= \left[\begin{smallmatrix} 5\\0\\1\\4\\0\end{smallmatrix}\right] +s\left[\begin{smallmatrix} -2\\1\\0\\0\\0\end{smallmatrix}\right] +t\left[\begin{smallmatrix} -6\\0\\2\\-3\\1\end{smallmatrix}\right], | * So $ \left[\begin{smallmatrix} x_1\\x_2\\x_3\\x_4 \\x_5\end{smallmatrix}\right]= \left[\begin{smallmatrix} 5\\0\\1\\4\\0\end{smallmatrix}\right] +s\left[\begin{smallmatrix} -2\\1\\0\\0\\0\end{smallmatrix}\right] +t\left[\begin{smallmatrix} -6\\0\\2\\-3\\1\end{smallmatrix}\right], | ||
| - | * (A $2$-dimensional | + | * 2 free vars, 5 vars in all |
| + | * Solution set is $2$-dimensional, in $5$-dimensional space $\mathbb{R}^5$. | ||
lecture_4_slides.1485969442.txt.gz · Last modified: by rupert