Error in obtaining the row-echelon form in calculations

[FabianMenekshi]

Describe the mistake
In Example 2.17 (Determining a Basis), there is an error at the end of the exercise when doing the calculations for the row-echelon form.

Location
Please provide the

1. Draft (2024-01-15) of “Mathematics for Machine Learning”
2. Chapter 2.6.1
3. page 46
4. Equation number: Right after 2.83

Proposed solution
This is the correct matrix in latex:
[
\begin{bmatrix}
1 & 2 & 3 & -1 \
0 & 1 & 2 & -2 \
0 & 0 & 0 & 0 \
0 & 0 & 0 & 1 \
0 & 0 & 0 & 0 \
\end{bmatrix}
]