Gaussian Elimination/Examples/Arbitrary Matrix 7/Mistake

Source Work

1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.): 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}$

Sources

• 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.2$ Elementary Row Operations on Matrices: Exercises $1.2$: $1 \ \text {(vi)}$