Find Reduced Row Echelon Form [[-6,8,0,0],[4,1,9,2]]

$[\begin{array}{c} - 6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \end{array}]$

Step 1

Perform the row operation $R_{1} = - \frac{1}{6} R_{1}$ 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 $R_{1} = - \frac{1}{6} R_{1}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} - \frac{1}{6} R_{1} & - \frac{1}{6} R_{1} & - \frac{1}{6} R_{1} & - \frac{1}{6} R_{1} \\ 4 & 1 & 9 & 2 \end{array}]$

$R_{1} = - \frac{1}{6} R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = - \frac{1}{6} R_{1}$ .

$[\begin{array}{c} (- \frac{1}{6}) \cdot (- 6) & (- \frac{1}{6}) \cdot (8) & (- \frac{1}{6}) \cdot (0) & (- \frac{1}{6}) \cdot (0) \\ 4 & 1 & 9 & 2 \end{array}]$

$R_{1} = - \frac{1}{6} R_{1}$

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

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ 4 & 1 & 9 & 2 \end{array}]$

Step 2

Perform the row operation $R_{2} = - 4 \cdot R_{1} + R_{2}$ 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 $R_{2} = - 4 \cdot R_{1} + R_{2}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ - 4 \cdot R_{1} + R_{2} & - 4 \cdot R_{1} + R_{2} & - 4 \cdot R_{1} + R_{2} & - 4 \cdot R_{1} + R_{2} \end{array}]$

$R_{2} = - 4 \cdot R_{1} + R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = - 4 \cdot R_{1} + R_{2}$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ (- 4) \cdot (1) + 4 & (- 4) \cdot (- \frac{4}{3}) + 1 & (- 4) \cdot (0) + 9 & (- 4) \cdot (0) + 2 \end{array}]$

$R_{2} = - 4 \cdot R_{1} + R_{2}$

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

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ 0 & \frac{19}{3} & 9 & 2 \end{array}]$

Step 3

Perform the row operation $R_{2} = \frac{3}{19} R_{2}$ 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 $R_{2} = \frac{3}{19} R_{2}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ \frac{3}{19} R_{2} & \frac{3}{19} R_{2} & \frac{3}{19} R_{2} & \frac{3}{19} R_{2} \end{array}]$

$R_{2} = \frac{3}{19} R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = \frac{3}{19} R_{2}$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ (\frac{3}{19}) \cdot (0) & (\frac{3}{19}) \cdot (\frac{19}{3}) & (\frac{3}{19}) \cdot (9) & (\frac{3}{19}) \cdot (2) \end{array}]$

$R_{2} = \frac{3}{19} R_{2}$

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

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ 0 & 1 & \frac{27}{19} & \frac{6}{19} \end{array}]$

Step 4

Perform the row operation $R_{1} = \frac{4}{3} R_{2} + R_{1}$ 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 $R_{1} = \frac{4}{3} R_{2} + R_{1}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} \frac{4}{3} R_{2} + R_{1} & \frac{4}{3} R_{2} + R_{1} & \frac{4}{3} R_{2} + R_{1} & \frac{4}{3} R_{2} + R_{1} \\ 0 & 1 & \frac{27}{19} & \frac{6}{19} \end{array}]$

$R_{1} = \frac{4}{3} R_{2} + R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = \frac{4}{3} R_{2} + R_{1}$ .

$[\begin{array}{c} (\frac{4}{3}) \cdot (0) + 1 & (\frac{4}{3}) \cdot (1) - \frac{4}{3} & (\frac{4}{3}) \cdot (\frac{27}{19}) + 0 & (\frac{4}{3}) \cdot (\frac{6}{19}) + 0 \\ 0 & 1 & \frac{27}{19} & \frac{6}{19} \end{array}]$

$R_{1} = \frac{4}{3} R_{2} + R_{1}$

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

$[\begin{array}{c} 1 & 0 & \frac{36}{19} & \frac{8}{19} \\ 0 & 1 & \frac{27}{19} & \frac{6}{19} \end{array}]$

Find Reduced Row Echelon Form [[-6,8,0,0],[4,1,9,2]]

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