Find Reduced Row Echelon Form [[2,7,48],[3,-12,27]]

$[\begin{array}{c} 2 & 7 & 48 \\ 3 & - 12 & 27 \end{array}]$

Perform the row operation $R_{1} = \frac{1}{2} R_{1}$ on $R_{1}$ (row $1$ ) in order to convert some elements in the row to $1$ .

Replace $R_{1}$ (row $1$ ) with the row operation $R_{1} = \frac{1}{2} R_{1}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} \frac{1}{2} R_{1} & \frac{1}{2} R_{1} & \frac{1}{2} R_{1} \\ 3 & - 12 & 27 \end{array}]$

$R_{1} = \frac{1}{2} R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = \frac{1}{2} R_{1}$ .

$[\begin{array}{c} (\frac{1}{2}) \cdot (2) & (\frac{1}{2}) \cdot (7) & (\frac{1}{2}) \cdot (48) \\ 3 & - 12 & 27 \end{array}]$

$R_{1} = \frac{1}{2} R_{1}$

Simplify $R_{1}$ (row $1$ ).

$[\begin{array}{c} 1 & \frac{7}{2} & 24 \\ 3 & - 12 & 27 \end{array}]$

Perform the row operation $R_{2} = - 3 \cdot R_{1} + R_{2}$ on $R_{2}$ (row $2$ ) in order to convert some elements in the row to $0$ .

Replace $R_{2}$ (row $2$ ) with the row operation $R_{2} = - 3 \cdot R_{1} + R_{2}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} 1 & \frac{7}{2} & 24 \\ - 3 \cdot R_{1} + R_{2} & - 3 \cdot R_{1} + R_{2} & - 3 \cdot R_{1} + R_{2} \end{array}]$

$R_{2} = - 3 \cdot R_{1} + R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = - 3 \cdot R_{1} + R_{2}$ .

$[\begin{array}{c} 1 & \frac{7}{2} & 24 \\ (- 3) \cdot (1) + 3 & (- 3) \cdot (\frac{7}{2}) - 12 & (- 3) \cdot (24) + 27 \end{array}]$

$R_{2} = - 3 \cdot R_{1} + R_{2}$

Simplify $R_{2}$ (row $2$ ).

$[\begin{array}{c} 1 & \frac{7}{2} & 24 \\ 0 & - \frac{45}{2} & - 45 \end{array}]$

Perform the row operation $R_{2} = - \frac{2}{45} R_{2}$ on $R_{2}$ (row $2$ ) in order to convert some elements in the row to $1$ .

Replace $R_{2}$ (row $2$ ) with the row operation $R_{2} = - \frac{2}{45} R_{2}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} 1 & \frac{7}{2} & 24 \\ - \frac{2}{45} R_{2} & - \frac{2}{45} R_{2} & - \frac{2}{45} R_{2} \end{array}]$

$R_{2} = - \frac{2}{45} R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = - \frac{2}{45} R_{2}$ .

$[\begin{array}{c} 1 & \frac{7}{2} & 24 \\ (- \frac{2}{45}) \cdot (0) & (- \frac{2}{45}) \cdot (- \frac{45}{2}) & (- \frac{2}{45}) \cdot (- 45) \end{array}]$

$R_{2} = - \frac{2}{45} R_{2}$

Simplify $R_{2}$ (row $2$ ).

$[\begin{array}{c} 1 & \frac{7}{2} & 24 \\ 0 & 1 & 2 \end{array}]$

Perform the row operation $R_{1} = - \frac{7}{2} R_{2} + R_{1}$ on $R_{1}$ (row $1$ ) in order to convert some elements in the row to $0$ .

Replace $R_{1}$ (row $1$ ) with the row operation $R_{1} = - \frac{7}{2} R_{2} + R_{1}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} - \frac{7}{2} R_{2} + R_{1} & - \frac{7}{2} R_{2} + R_{1} & - \frac{7}{2} R_{2} + R_{1} \\ 0 & 1 & 2 \end{array}]$

$R_{1} = - \frac{7}{2} R_{2} + R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = - \frac{7}{2} R_{2} + R_{1}$ .

$[\begin{array}{c} (- \frac{7}{2}) \cdot (0) + 1 & (- \frac{7}{2}) \cdot (1) + \frac{7}{2} & (- \frac{7}{2}) \cdot (2) + 24 \\ 0 & 1 & 2 \end{array}]$

$R_{1} = - \frac{7}{2} R_{2} + R_{1}$

Simplify $R_{1}$ (row $1$ ).

$[\begin{array}{c} 1 & 0 & 17 \\ 0 & 1 & 2 \end{array}]$

Find Reduced Row Echelon Form [[2,7,48],[3,-12,27]]

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