Use the Gauss elimination method to solve the system of equations:

x₁ - 2x₂ + x₃ = 0 ; 2x₁ + x₂ - 3x₃ = 5 ; 4x₁ -7x₂ + x₃ = -1

To solve the system of equations using Gauss elimination, we represent the system in augmented matrix form:

\[
\begin{bmatrix}
1 & -2 & 1 & | & 0 \\
2 & 1 & -3 & | & 5 \\
4 & -7 & 1 & | & -1
\end{bmatrix}
\]

Step 1: Forward Elimination

We will perform row operations to convert the matrix to upper triangular form.

1. Use the first row to eliminate the first variable from the second and third __________ __________ ____ __________ ______.
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