Find Reduced Row Echelon Form [[1,0,-1,19/3],[-2,1,5,-47/3],[4,0,-4,76/3]]

$[\begin{array}{c} 1 & 0 & - 1 & \frac{19}{3} \\ - 2 & 1 & 5 & - \frac{47}{3} \\ 4 & 0 & - 4 & \frac{76}{3} \end{array}]$

Step 1

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

$[\begin{array}{c} 1 & 0 & - 1 & \frac{19}{3} \\ 2 \cdot R_{1} + R_{2} & 2 \cdot R_{1} + R_{2} & 2 \cdot R_{1} + R_{2} & 2 \cdot R_{1} + R_{2} \\ 4 & 0 & - 4 & \frac{76}{3} \end{array}]$

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

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

$[\begin{array}{c} 1 & 0 & - 1 & \frac{19}{3} \\ (2) \cdot (1) - 2 & (2) \cdot (0) + 1 & (2) \cdot (- 1) + 5 & (2) \cdot (\frac{19}{3}) - \frac{47}{3} \\ 4 & 0 & - 4 & \frac{76}{3} \end{array}]$

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

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

$[\begin{array}{c} 1 & 0 & - 1 & \frac{19}{3} \\ 0 & 1 & 3 & - 3 \\ 4 & 0 & - 4 & \frac{76}{3} \end{array}]$

Step 2

Perform the row operation $R_{3} = - 4 \cdot R_{1} + R_{3}$ on $R_{3}$ (row $3$ ) in order to convert some elements in the row to $0$ .

Replace $R_{3}$ (row $3$ ) with the row operation $R_{3} = - 4 \cdot R_{1} + R_{3}$ in order to convert some elements in the row to the desired value $0$ .

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

$R_{3} = - 4 \cdot R_{1} + R_{3}$

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

$[\begin{array}{c} 1 & 0 & - 1 & \frac{19}{3} \\ 0 & 1 & 3 & - 3 \\ (- 4) \cdot (1) + 4 & (- 4) \cdot (0) + 0 & (- 4) \cdot (- 1) - 4 & (- 4) \cdot (\frac{19}{3}) + \frac{76}{3} \end{array}]$

$R_{3} = - 4 \cdot R_{1} + R_{3}$

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

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

Find Reduced Row Echelon Form [[1,0,-1,19/3],[-2,1,5,-47/3],[4,0,-4,76/3]]

Related Questions

Support LCMGCF.com by disabling your adblocker.