Find Reduced Row Echelon Form [[1,1,0],[1,0,1],[1,0,1],[2,1,0],[2,1,0]]

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

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

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

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

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

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

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

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

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

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

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

Tap for more steps...

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

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

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

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

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

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

Simplify $R_{3}$ (row $3$ ).

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

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

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

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

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

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

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

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

Simplify $R_{4}$ (row $4$ ).

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

Perform the row operation $R_{5} = - 2 \cdot R_{1} + R_{5}$ on $R_{5}$ (row $5$ ) in order to convert some elements in the row to $0$ .

Tap for more steps...

Replace $R_{5}$ (row $5$ ) with the row operation $R_{5} = - 2 \cdot R_{1} + R_{5}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} 1 & 1 & 0 \\ 0 & - 1 & 1 \\ 0 & - 1 & 1 \\ 0 & - 1 & 0 \\ - 2 \cdot R_{1} + R_{5} & - 2 \cdot R_{1} + R_{5} & - 2 \cdot R_{1} + R_{5} \end{array}]$

$R_{5} = - 2 \cdot R_{1} + R_{5}$

Replace $R_{5}$ (row $5$ ) with the actual values of the elements for the row operation $R_{5} = - 2 \cdot R_{1} + R_{5}$ .

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

$R_{5} = - 2 \cdot R_{1} + R_{5}$

Simplify $R_{5}$ (row $5$ ).

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

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

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

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

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

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

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

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

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

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

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

Tap for more steps...

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

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

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

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

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

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

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

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

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

Tap for more steps...

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

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

$R_{3} = R_{2} + R_{3}$

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

$[\begin{array}{c} 1 & 0 & 1 \\ 0 & 1 & - 1 \\ 0 + 0 & 1 - 1 & - 1 + 1 \\ 0 & - 1 & 0 \\ 0 & - 1 & 0 \end{array}]$

$R_{3} = R_{2} + R_{3}$

Simplify $R_{3}$ (row $3$ ).

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

Perform the row operation $R_{4} = R_{2} + R_{4}$ on $R_{4}$ (row $4$ ) in order to convert some elements in the row to $0$ .

Tap for more steps...

Replace $R_{4}$ (row $4$ ) with the row operation $R_{4} = R_{2} + R_{4}$ in order to convert some elements in the row to the desired value $0$ .

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

$R_{4} = R_{2} + R_{4}$

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

$[\begin{array}{c} 1 & 0 & 1 \\ 0 & 1 & - 1 \\ 0 & 0 & 0 \\ 0 + 0 & 1 - 1 & - 1 + 0 \\ 0 & - 1 & 0 \end{array}]$

$R_{4} = R_{2} + R_{4}$

Simplify $R_{4}$ (row $4$ ).

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

Perform the row operation $R_{5} = R_{2} + R_{5}$ on $R_{5}$ (row $5$ ) in order to convert some elements in the row to $0$ .

Tap for more steps...

Replace $R_{5}$ (row $5$ ) with the row operation $R_{5} = R_{2} + R_{5}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} 1 & 0 & 1 \\ 0 & 1 & - 1 \\ 0 & 0 & 0 \\ 0 & 0 & - 1 \\ R_{2} + R_{5} & R_{2} + R_{5} & R_{2} + R_{5} \end{array}]$

$R_{5} = R_{2} + R_{5}$

Replace $R_{5}$ (row $5$ ) with the actual values of the elements for the row operation $R_{5} = R_{2} + R_{5}$ .

$[\begin{array}{c} 1 & 0 & 1 \\ 0 & 1 & - 1 \\ 0 & 0 & 0 \\ 0 & 0 & - 1 \\ 0 + 0 & 1 - 1 & - 1 + 0 \end{array}]$

$R_{5} = R_{2} + R_{5}$

Simplify $R_{5}$ (row $5$ ).

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

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