Chapter 8, Problem 9RE

To determine

Write given matrix in Row-Echelon Form.

Answer to Problem 9RE

This matrix can't be converted to the row echelon form

Explanation of Solution

Given:

The matrix:

  $\left[\begin{array}{ccc}0& 1& 1\\ 1& 2& 3\\ 2& 2& 2\end{array}\right]$

Let consider the following matrix

  $\left[\begin{array}{ccc}0& 1& 1\\ 1& 2& 3\\ 2& 2& 2\end{array}\right]$

This matrix has the first element of first row as zero.

So, all the below non-zero elements can't be converted to zero.

So, there are non-zero elements to the left of the first non-zero element of the first row.

Hence, this matrix can't be converted to the row echelon form.