Find Reduced Row Echelon Form [[9,1,-1,9],[8,8,-7,8]]

$[\begin{array}{c} 9 & 1 & - 1 & 9 \\ 8 & 8 & - 7 & 8 \end{array}]$

Step 1

Perform the row operation $R_{1} = \frac{1}{9} R_{1}$ 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 $R_{1} = \frac{1}{9} R_{1}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} \frac{1}{9} R_{1} & \frac{1}{9} R_{1} & \frac{1}{9} R_{1} & \frac{1}{9} R_{1} \\ 8 & 8 & - 7 & 8 \end{array}]$

$R_{1} = \frac{1}{9} R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = \frac{1}{9} R_{1}$ .

$[\begin{array}{c} (\frac{1}{9}) \cdot (9) & (\frac{1}{9}) \cdot (1) & (\frac{1}{9}) \cdot (- 1) & (\frac{1}{9}) \cdot (9) \\ 8 & 8 & - 7 & 8 \end{array}]$

$R_{1} = \frac{1}{9} R_{1}$

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

$[\begin{array}{c} 1 & \frac{1}{9} & - \frac{1}{9} & 1 \\ 8 & 8 & - 7 & 8 \end{array}]$

Step 2

Perform the row operation $R_{2} = - 8 \cdot R_{1} + R_{2}$ 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 $R_{2} = - 8 \cdot R_{1} + R_{2}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} 1 & \frac{1}{9} & - \frac{1}{9} & 1 \\ - 8 \cdot R_{1} + R_{2} & - 8 \cdot R_{1} + R_{2} & - 8 \cdot R_{1} + R_{2} & - 8 \cdot R_{1} + R_{2} \end{array}]$

$R_{2} = - 8 \cdot R_{1} + R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = - 8 \cdot R_{1} + R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{9} & - \frac{1}{9} & 1 \\ (- 8) \cdot (1) + 8 & (- 8) \cdot (\frac{1}{9}) + 8 & (- 8) \cdot (- \frac{1}{9}) - 7 & (- 8) \cdot (1) + 8 \end{array}]$

$R_{2} = - 8 \cdot R_{1} + R_{2}$

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

$[\begin{array}{c} 1 & \frac{1}{9} & - \frac{1}{9} & 1 \\ 0 & \frac{64}{9} & - \frac{55}{9} & 0 \end{array}]$

Step 3

Perform the row operation $R_{2} = \frac{9}{64} R_{2}$ 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 $R_{2} = \frac{9}{64} R_{2}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} 1 & \frac{1}{9} & - \frac{1}{9} & 1 \\ \frac{9}{64} R_{2} & \frac{9}{64} R_{2} & \frac{9}{64} R_{2} & \frac{9}{64} R_{2} \end{array}]$

$R_{2} = \frac{9}{64} R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = \frac{9}{64} R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{9} & - \frac{1}{9} & 1 \\ (\frac{9}{64}) \cdot (0) & (\frac{9}{64}) \cdot (\frac{64}{9}) & (\frac{9}{64}) \cdot (- \frac{55}{9}) & (\frac{9}{64}) \cdot (0) \end{array}]$

$R_{2} = \frac{9}{64} R_{2}$

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

$[\begin{array}{c} 1 & \frac{1}{9} & - \frac{1}{9} & 1 \\ 0 & 1 & - \frac{55}{64} & 0 \end{array}]$

Step 4

Perform the row operation $R_{1} = - \frac{1}{9} R_{2} + R_{1}$ 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 $R_{1} = - \frac{1}{9} R_{2} + R_{1}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} - \frac{1}{9} R_{2} + R_{1} & - \frac{1}{9} R_{2} + R_{1} & - \frac{1}{9} R_{2} + R_{1} & - \frac{1}{9} R_{2} + R_{1} \\ 0 & 1 & - \frac{55}{64} & 0 \end{array}]$

$R_{1} = - \frac{1}{9} R_{2} + R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = - \frac{1}{9} R_{2} + R_{1}$ .

$[\begin{array}{c} (- \frac{1}{9}) \cdot (0) + 1 & (- \frac{1}{9}) \cdot (1) + \frac{1}{9} & (- \frac{1}{9}) \cdot (- \frac{55}{64}) - \frac{1}{9} & (- \frac{1}{9}) \cdot (0) + 1 \\ 0 & 1 & - \frac{55}{64} & 0 \end{array}]$

$R_{1} = - \frac{1}{9} R_{2} + R_{1}$

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

$[\begin{array}{c} 1 & 0 & - \frac{1}{64} & 1 \\ 0 & 1 & - \frac{55}{64} & 0 \end{array}]$

Find Reduced Row Echelon Form [[9,1,-1,9],[8,8,-7,8]]

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