Find Reduced Row Echelon Form [[1,-2,4,11],[0,1,2,11],[0,0,1,4]]

$[\begin{array}{c} 1 & - 2 & 4 & 11 \\ 0 & 1 & 2 & 11 \\ 0 & 0 & 1 & 4 \end{array}]$

Step 1

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

$[\begin{array}{c} 2 \cdot R_{2} + R_{1} & 2 \cdot R_{2} + R_{1} & 2 \cdot R_{2} + R_{1} & 2 \cdot R_{2} + R_{1} \\ 0 & 1 & 2 & 11 \\ 0 & 0 & 1 & 4 \end{array}]$

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

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

$[\begin{array}{c} (2) \cdot (0) + 1 & (2) \cdot (1) - 2 & (2) \cdot (2) + 4 & (2) \cdot (11) + 11 \\ 0 & 1 & 2 & 11 \\ 0 & 0 & 1 & 4 \end{array}]$

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

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

$[\begin{array}{c} 1 & 0 & 8 & 33 \\ 0 & 1 & 2 & 11 \\ 0 & 0 & 1 & 4 \end{array}]$

Step 2

Perform the row operation $R_{1} = - 8 \cdot R_{3} + R_{1}$ 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 $R_{1} = - 8 \cdot R_{3} + R_{1}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} - 8 \cdot R_{3} + R_{1} & - 8 \cdot R_{3} + R_{1} & - 8 \cdot R_{3} + R_{1} & - 8 \cdot R_{3} + R_{1} \\ 0 & 1 & 2 & 11 \\ 0 & 0 & 1 & 4 \end{array}]$

$R_{1} = - 8 \cdot R_{3} + R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = - 8 \cdot R_{3} + R_{1}$ .

$[\begin{array}{c} (- 8) \cdot (0) + 1 & (- 8) \cdot (0) + 0 & (- 8) \cdot (1) + 8 & (- 8) \cdot (4) + 33 \\ 0 & 1 & 2 & 11 \\ 0 & 0 & 1 & 4 \end{array}]$

$R_{1} = - 8 \cdot R_{3} + R_{1}$

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

$[\begin{array}{c} 1 & 0 & 0 & 1 \\ 0 & 1 & 2 & 11 \\ 0 & 0 & 1 & 4 \end{array}]$

Step 3

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

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

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

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

$[\begin{array}{c} 1 & 0 & 0 & 1 \\ (- 2) \cdot (0) + 0 & (- 2) \cdot (0) + 1 & (- 2) \cdot (1) + 2 & (- 2) \cdot (4) + 11 \\ 0 & 0 & 1 & 4 \end{array}]$

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

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

$[\begin{array}{c} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & 4 \end{array}]$

Find Reduced Row Echelon Form [[1,-2,4,11],[0,1,2,11],[0,0,1,4]]

Related Questions

Support LCMGCF.com by disabling your adblocker.