# How do you write the matrix [(1, 1, 0, 5), (-2, -1, 2, -10), (3, 6, 7, 14)] using the row echelon form?

Feb 3, 2018

The row echelon form is $= \left(\begin{matrix}1 & 1 & 0 & 5 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 1 & - 1\end{matrix}\right)$

#### Explanation:

A matrix is in row echelon form if :

• Each row has a 1 as first non-zero entry

• For 2 succesive rows, the leading 1 in higher row is farther left than the leading 1 in the lower row

Perform the following operations on the rows

$A = \left(\begin{matrix}1 & 1 & 0 & 5 \\ - 2 & - 1 & 2 & - 10 \\ 3 & 6 & 7 & 14\end{matrix}\right)$

$\left(R 2 \leftarrow R 2 + 2 R 1\right)$ and $\left(R 3 \leftarrow R 3 - 3 R 1\right)$

$= \left(\begin{matrix}1 & 1 & 0 & 5 \\ 0 & 1 & 2 & 0 \\ 0 & 3 & 7 & - 1\end{matrix}\right)$

$\left(R 3 \leftarrow R 3 - 3 R 2\right)$

$= \left(\begin{matrix}1 & 1 & 0 & 5 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 1 & - 1\end{matrix}\right)$