# How do you write the matrix [(1, 2, -1, 3), (3, 7, -5, 14), (-2, -1, -3, 8)] using the row echelon form?

Apr 17, 2017

$\left[\begin{matrix}1 & 2 & - 1 & 3 \\ 3 & 7 & - 5 & 14 \\ - 2 & - 1 & - 3 & 8\end{matrix}\right]$

$R 2 \to R 2 - 3 R 1 \text{ & } R 3 \to R 3 + 2 R 1$

$\left[\begin{matrix}1 & 2 & - 1 & 3 \\ 0 & 1 & - 2 & 5 \\ 0 & 3 & - 5 & 14\end{matrix}\right]$

$R 3 \to R 3 - 3 R 2$

$\left[\begin{matrix}1 & 2 & - 1 & 3 \\ 0 & 1 & - 2 & 5 \\ 0 & 0 & 1 & - 1\end{matrix}\right]$

You now have the 3 pivots