Gaussian Elimination/Examples/Arbitrary Matrix 7/Mistake

Source Work
Chapter $1$: Linear Equations and Matrices:
 * $1.2$ Elementary Row Operations on Matrices:
 * Exercises $1.2$:
 * $1 \ \text {(vi)}$


 * Solutions to Exercises

Mistake

 * ''Find the reduced echelon matrices of the following matrices
 * ''(vi) $\begin {bmatrix}

1 & 1 -   \sqrt 2 &  0           &        \sqrt 2 \\ \sqrt 2    & -3             &  1 + \sqrt 2 & -1 - 2 \sqrt 2 \\ -1 &       \sqrt 2 & -1           &  1             \\ \sqrt 2 - 2 & -2 + 4 \sqrt 2 & -2 - \sqrt 2 & 3 +   \sqrt 2 \\ \end {bmatrix}$


 * Solutions to Exercises: ''Exercises $1.2 \ \text {(vi)}$: $\begin {bmatrix}

1 & 0 & 0 & 0 \\ 0 & 1 & 0 &  0 \\ 0 & 0 & 1 &  0 \\ 0 & 0 & 0 &  1 \\ \end {bmatrix}$

Correction
Evaluation according to Gaussian Elimination: Arbitrary Matrix $7$ gives the answer as:


 * $\begin {bmatrix}

1 & 0 & 1 - \sqrt 2 &  0 \\ 0 & 1 & -1          &  0 \\ 0 & 0 &  0           &  1 \\ 0 & 0 &  0           &  0 \\ \end {bmatrix}$