Question
If $A=\left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 3 & 4\end{array}\right]$, apply the transformation $C_1 \rightarrow C_1+2 C_3$.
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Answer
$\begin{array}{l}A=\left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 3 & 4\end{array}\right] \end{array} $
$ C_1 \rightarrow C_1+2 C_3$ gives
$ A \sim\left[\begin{array}{ccc}1+2(2) & 0 & 2 \\ 2+2(4) & 3 & 4\end{array}\right] $
$ A \sim\left[\begin{array}{ccc}5 & 0 & 2 \\ 10 & 3 & 4\end{array}\right]$
$ C_1 \rightarrow C_1+2 C_3$ gives
$ A \sim\left[\begin{array}{ccc}1+2(2) & 0 & 2 \\ 2+2(4) & 3 & 4\end{array}\right] $
$ A \sim\left[\begin{array}{ccc}5 & 0 & 2 \\ 10 & 3 & 4\end{array}\right]$
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