Find Reduced Row Echelon Form [[7,-3,7],[21,3,25]]

$[\begin{array}{c} 7 & - 3 & 7 \\ 21 & 3 & 25 \end{array}]$

Perform the row operation $R_{1} = \frac{1}{7} R_{1}$ 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 $R_{1} = \frac{1}{7} R_{1}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} \frac{1}{7} R_{1} & \frac{1}{7} R_{1} & \frac{1}{7} R_{1} \\ 21 & 3 & 25 \end{array}]$

$R_{1} = \frac{1}{7} R_{1}$

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

$[\begin{array}{c} (\frac{1}{7}) \cdot (7) & (\frac{1}{7}) \cdot (- 3) & (\frac{1}{7}) \cdot (7) \\ 21 & 3 & 25 \end{array}]$

$R_{1} = \frac{1}{7} R_{1}$

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

$[\begin{array}{c} 1 & - \frac{3}{7} & 1 \\ 21 & 3 & 25 \end{array}]$

Perform the row operation $R_{2} = - 21 \cdot R_{1} + R_{2}$ 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 $R_{2} = - 21 \cdot R_{1} + R_{2}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} 1 & - \frac{3}{7} & 1 \\ - 21 \cdot R_{1} + R_{2} & - 21 \cdot R_{1} + R_{2} & - 21 \cdot R_{1} + R_{2} \end{array}]$

$R_{2} = - 21 \cdot R_{1} + R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = - 21 \cdot R_{1} + R_{2}$ .

$[\begin{array}{c} 1 & - \frac{3}{7} & 1 \\ (- 21) \cdot (1) + 21 & (- 21) \cdot (- \frac{3}{7}) + 3 & (- 21) \cdot (1) + 25 \end{array}]$

$R_{2} = - 21 \cdot R_{1} + R_{2}$

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

$[\begin{array}{c} 1 & - \frac{3}{7} & 1 \\ 0 & 12 & 4 \end{array}]$

Perform the row operation $R_{2} = \frac{1}{12} R_{2}$ 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 $R_{2} = \frac{1}{12} R_{2}$ in order to convert some elements in the row to the desired value $1$ .

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

$R_{2} = \frac{1}{12} R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = \frac{1}{12} R_{2}$ .

$[\begin{array}{c} 1 & - \frac{3}{7} & 1 \\ (\frac{1}{12}) \cdot (0) & (\frac{1}{12}) \cdot (12) & (\frac{1}{12}) \cdot (4) \end{array}]$

$R_{2} = \frac{1}{12} R_{2}$

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

$[\begin{array}{c} 1 & - \frac{3}{7} & 1 \\ 0 & 1 & \frac{1}{3} \end{array}]$

Perform the row operation $R_{1} = \frac{3}{7} R_{2} + R_{1}$ 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 $R_{1} = \frac{3}{7} R_{2} + R_{1}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} \frac{3}{7} R_{2} + R_{1} & \frac{3}{7} R_{2} + R_{1} & \frac{3}{7} R_{2} + R_{1} \\ 0 & 1 & \frac{1}{3} \end{array}]$

$R_{1} = \frac{3}{7} R_{2} + R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = \frac{3}{7} R_{2} + R_{1}$ .

$[\begin{array}{c} (\frac{3}{7}) \cdot (0) + 1 & (\frac{3}{7}) \cdot (1) - \frac{3}{7} & (\frac{3}{7}) \cdot (\frac{1}{3}) + 1 \\ 0 & 1 & \frac{1}{3} \end{array}]$

$R_{1} = \frac{3}{7} R_{2} + R_{1}$

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

$[\begin{array}{c} 1 & 0 & \frac{8}{7} \\ 0 & 1 & \frac{1}{3} \end{array}]$

Find Reduced Row Echelon Form [[7,-3,7],[21,3,25]]

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