Find Reduced Row Echelon Form [[3,5,42],[6,5,54]]

$[\begin{array}{c} 3 & 5 & 42 \\ 6 & 5 & 54 \end{array}]$

Step 1

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

$[\begin{array}{c} \frac{1}{3} R_{1} & \frac{1}{3} R_{1} & \frac{1}{3} R_{1} \\ 6 & 5 & 54 \end{array}]$

$R_{1} = \frac{1}{3} R_{1}$

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

$[\begin{array}{c} (\frac{1}{3}) \cdot (3) & (\frac{1}{3}) \cdot (5) & (\frac{1}{3}) \cdot (42) \\ 6 & 5 & 54 \end{array}]$

$R_{1} = \frac{1}{3} R_{1}$

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

$[\begin{array}{c} 1 & \frac{5}{3} & 14 \\ 6 & 5 & 54 \end{array}]$

Step 2

Perform the row operation $R_{2} = - 6 \cdot R_{1} + R_{2}$ 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 $R_{2} = - 6 \cdot R_{1} + R_{2}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} 1 & \frac{5}{3} & 14 \\ - 6 \cdot R_{1} + R_{2} & - 6 \cdot R_{1} + R_{2} & - 6 \cdot R_{1} + R_{2} \end{array}]$

$R_{2} = - 6 \cdot R_{1} + R_{2}$

Replace $R_{2}$ (row $2$ ) with the actual values of the elements for the row operation $R_{2} = - 6 \cdot R_{1} + R_{2}$ .

$[\begin{array}{c} 1 & \frac{5}{3} & 14 \\ (- 6) \cdot (1) + 6 & (- 6) \cdot (\frac{5}{3}) + 5 & (- 6) \cdot (14) + 54 \end{array}]$

$R_{2} = - 6 \cdot R_{1} + R_{2}$

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

$[\begin{array}{c} 1 & \frac{5}{3} & 14 \\ 0 & - 5 & - 30 \end{array}]$

Step 3

Perform the row operation $R_{2} = - \frac{1}{5} R_{2}$ 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 $R_{2} = - \frac{1}{5} R_{2}$ in order to convert some elements in the row to the desired value $1$ .

$[\begin{array}{c} 1 & \frac{5}{3} & 14 \\ - \frac{1}{5} R_{2} & - \frac{1}{5} R_{2} & - \frac{1}{5} R_{2} \end{array}]$

$R_{2} = - \frac{1}{5} R_{2}$

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

$[\begin{array}{c} 1 & \frac{5}{3} & 14 \\ (- \frac{1}{5}) \cdot (0) & (- \frac{1}{5}) \cdot (- 5) & (- \frac{1}{5}) \cdot (- 30) \end{array}]$

$R_{2} = - \frac{1}{5} R_{2}$

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

$[\begin{array}{c} 1 & \frac{5}{3} & 14 \\ 0 & 1 & 6 \end{array}]$

Step 4

Perform the row operation $R_{1} = - \frac{5}{3} R_{2} + R_{1}$ 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 $R_{1} = - \frac{5}{3} R_{2} + R_{1}$ in order to convert some elements in the row to the desired value $0$ .

$[\begin{array}{c} - \frac{5}{3} R_{2} + R_{1} & - \frac{5}{3} R_{2} + R_{1} & - \frac{5}{3} R_{2} + R_{1} \\ 0 & 1 & 6 \end{array}]$

$R_{1} = - \frac{5}{3} R_{2} + R_{1}$

Replace $R_{1}$ (row $1$ ) with the actual values of the elements for the row operation $R_{1} = - \frac{5}{3} R_{2} + R_{1}$ .

$[\begin{array}{c} (- \frac{5}{3}) \cdot (0) + 1 & (- \frac{5}{3}) \cdot (1) + \frac{5}{3} & (- \frac{5}{3}) \cdot (6) + 14 \\ 0 & 1 & 6 \end{array}]$

$R_{1} = - \frac{5}{3} R_{2} + R_{1}$

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

$[\begin{array}{c} 1 & 0 & 4 \\ 0 & 1 & 6 \end{array}]$

Find Reduced Row Echelon Form [[3,5,42],[6,5,54]]

Related Questions

Support LCMGCF.com by disabling your adblocker.