Find Reduced Row Echelon Form [[-15,-3,-63],[6,1,26]]

$[\begin{array}{c} - 15 & - 3 & - 63 \\ 6 & 1 & 26 \end{array}]$

Step 1

Multiply each element of $R_{1}$ by $- \frac{1}{15}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{15} \cdot - 15 & - \frac{1}{15} \cdot - 3 & - \frac{1}{15} \cdot - 63 \\ 6 & 1 & 26 \end{array}]$

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{21}{5} \\ 6 & 1 & 26 \end{array}]$

Step 2

Perform the row operation $R_{2} = R_{2} - 6 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{21}{5} \\ 6 - 6 \cdot 1 & 1 - 6 (\frac{1}{5}) & 26 - 6 (\frac{21}{5}) \end{array}]$

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{21}{5} \\ 0 & - \frac{1}{5} & \frac{4}{5} \end{array}]$

Step 3

Multiply each element of $R_{2}$ by $- 5$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{21}{5} \\ - 5 \cdot 0 & - 5 (- \frac{1}{5}) & - 5 (\frac{4}{5}) \end{array}]$

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{21}{5} \\ 0 & 1 & - 4 \end{array}]$

Step 4

Perform the row operation $R_{1} = R_{1} - \frac{1}{5} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{1}{5} \cdot 0 & \frac{1}{5} - \frac{1}{5} \cdot 1 & \frac{21}{5} - \frac{1}{5} \cdot - 4 \\ 0 & 1 & - 4 \end{array}]$

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 5 \\ 0 & 1 & - 4 \end{array}]$