Possible error in the row-reduction example in the "Matrix Decompositions" chapter

Description

In the "Matrix Decompositions" chapter, I believe there is an error in the Gaussian elimination example.

The final entry in the row-echelon matrix appears to be written as $-2$, but I think it should be $0$.

Derivation

The original matrix is:

$$ \begin{bmatrix} 2 & 1 & 5 \ 4 & 3 & 7 \ 6 & 5 & 9 \end{bmatrix} $$

First, apply:

$$ R_2 \leftarrow R_2 - 2R_1 $$

and:

$$ R_3 \leftarrow R_3 - 3R_1. $$

This gives:

$$ \begin{bmatrix} 2 & 1 & 5 \ 0 & 1 & -3 \ 0 & 2 & -6 \end{bmatrix}. $$

Then apply:

$$ R_3 \leftarrow R_3 - 2R_2. $$

Since:

$$ [0,2,-6]-2[0,1,-3]=[0,0,0], $$

the correct row-echelon form should be:

$$ \begin{bmatrix} 2 & 1 & 5 \ 0 & 1 & -3 \ 0 & 0 & 0 \end{bmatrix}. $$

Therefore, the value $-2$ shown in the image should be $0$.

This is also consistent with the nonzero solution:

$$ \mathbf{x}= t \begin{bmatrix} -4 \ 3 \ 1 \end{bmatrix}, \qquad t\in\mathbb{R}. $$

For example, when $t=1$:

$$ \begin{bmatrix} 2 & 1 & 5 \ 4 & 3 & 7 \ 6 & 5 & 9 \end{bmatrix} \begin{bmatrix} -4 \ 3 \ 1 \end{bmatrix}= \begin{bmatrix} 0 \ 0 \ 0 \end{bmatrix}. $$