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Compute ref(A) where A = [itex]

\begin{bmatrix}

1 & 2\\

3 & 8

\end{bmatrix}

[/itex]

[tex]\\ \begin{bmatrix}1 & 2\\ 3 & 8\end{bmatrix} \ r_2 \rightarrow r_2 - 3 \times r_1 \\ \\ \begin{bmatrix}1 & 2\\ 0 & 2 \end{bmatrix} \ r_2 \rightarrow \frac{1}{2} \times r_2 \\ \\ \begin{bmatrix}1 & 2\\ 0 & 1 \end{bmatrix}

[/tex]

Now I would have thought that this last matrix, A = [itex]

\begin{bmatrix}

1 & 2\\

0 & 1

\end{bmatrix}

[/itex] would be the ref(A).

But my TI-89 gives ref(A) = [itex]

\begin{bmatrix}

1 & \frac{8}{3}\\

0 & 1

\end{bmatrix}

[/itex] and this is not the rref(A), the rref(A) is just the 2x2 identity matrix.