# How do you write the matrix [(1, -1, -1, 1), (5, -4, 1, 8), (-6, 8, 18, 0)] using the row echelon form?

Jul 10, 2018

The matrix is $\left(\begin{matrix}1 & 0 & 5 & 4 \\ 0 & 1 & 6 & 3 \\ 0 & 0 & 0 & 0\end{matrix}\right)$

#### Explanation:

Perform the row operations on the matrix

$A = \left(\begin{matrix}1 & - 1 & - 1 & 1 \\ 5 & - 4 & 1 & 8 \\ - 6 & 8 & 18 & 0\end{matrix}\right)$

The pivot is in the first column of the first row

Eliminate the first column

$R 2 \leftarrow R 2 - 5 R 1$ and $R 3 \leftarrow R 3 + 6 R 1$

$\left(\begin{matrix}1 & - 1 & - 1 & 1 \\ 0 & 1 & 6 & 3 \\ 0 & 2 & 12 & 6\end{matrix}\right)$

Find the pivot in the second column and in in the second row

Eliminate the second column

$R 1 \leftarrow R 1 + R 2$ and $R 3 \leftarrow R 3 - 2 R 2$

$\left(\begin{matrix}1 & 0 & 5 & 4 \\ 0 & 1 & 6 & 3 \\ 0 & 0 & 0 & 0\end{matrix}\right)$