Apply the given elementary transformation on each of the following matrices.
$A = [\begin{matrix} 1 & 0 - 1 & 3 \end{matrix}], R_{1} \leftrightarrow R_{2}$

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Solution

$A = [\begin{matrix} 1 & 0 - 1 & 3 \end{matrix}]$

$R_{1} \leftrightarrow R_{2}$

$= [\begin{matrix} - 1 & 3 1 & 0 \end{matrix}]$ .

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R_{2}

\to

R_{2}

R_{3}

R_{1}

\to

R_{1} - R_{2}

R_{3}

\to

R_{3}

R_{2}

[\begin{matrix} 1 & 2 & 0 \\ 2 & 3 & - 1 \\ 1 & - 1 & 3 \end{matrix}]

[\begin{matrix} 1 & 3 & - 2 \\ - 3 & 0 & - 1 \\ 2 & 1 & 0 \end{matrix}]

[\begin{matrix} 1 & 1 & 2 \\ 3 & 1 & 1 \\ 2 & 3 & 1 \end{matrix}]

[\begin{matrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{matrix}]

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