Find Reduced Row Echelon Form [[8,5,38],[3,2,14]]

$[\begin{array}{c} 8 & 5 & 38 \\ 3 & 2 & 14 \end{array}]$

Step 1

Multiply each element of $R_{1}$ by $\frac{1}{8}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{8}{8} & \frac{5}{8} & \frac{38}{8} \\ 3 & 2 & 14 \end{array}]$

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & \frac{5}{8} & \frac{19}{4} \\ 3 & 2 & 14 \end{array}]$

Step 2

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{5}{8} & \frac{19}{4} \\ 3 - 3 \cdot 1 & 2 - 3 (\frac{5}{8}) & 14 - 3 (\frac{19}{4}) \end{array}]$

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{5}{8} & \frac{19}{4} \\ 0 & \frac{1}{8} & - \frac{1}{4} \end{array}]$

Step 3

Multiply each element of $R_{2}$ by $8$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{5}{8} & \frac{19}{4} \\ 8 \cdot 0 & 8 (\frac{1}{8}) & 8 (- \frac{1}{4}) \end{array}]$

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{5}{8} & \frac{19}{4} \\ 0 & 1 & - 2 \end{array}]$

Step 4

Perform the row operation $R_{1} = R_{1} - \frac{5}{8} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{5}{8} \cdot 0 & \frac{5}{8} - \frac{5}{8} \cdot 1 & \frac{19}{4} - \frac{5}{8} \cdot - 2 \\ 0 & 1 & - 2 \end{array}]$

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 6 \\ 0 & 1 & - 2 \end{array}]$