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This is a very basic question that I've been too embarassed to ask my elementary linear algebra teacher this far into the course:

Lets say we have a matrix

[tex]

\begin{pmatrix}

1 & 2 \\

2 & 1 \\

\end{pmatrix}

[/tex]

Why can't we do something like ##R_2 - 2R_1## and ##R_1 - \frac {1}{2} R_2## at the same time? We would be multiplying each row by a multiple of the other. My teacher always does more than one row operation at a time. What is it that I'm missing?

Lets say we have a matrix

[tex]

\begin{pmatrix}

1 & 2 \\

2 & 1 \\

\end{pmatrix}

[/tex]

Why can't we do something like ##R_2 - 2R_1## and ##R_1 - \frac {1}{2} R_2## at the same time? We would be multiplying each row by a multiple of the other. My teacher always does more than one row operation at a time. What is it that I'm missing?

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