Examples

$[\begin{array}{c} 7 & 2 & 2 \\ 2 & 2 & 7 \end{array}]$

Step 1

Multiply each element of $R_{1}$ by $\frac{1}{7}$ to make the entry at $1, 1$ a $1$ .

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Step 1.1

Multiply each element of $R_{1}$ by $\frac{1}{7}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{7}{7} & \frac{2}{7} & \frac{2}{7} \\ 2 & 2 & 7 \end{array}]$

Step 1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{2}{7} \\ 2 & 2 & 7 \end{array}]$

Step 2

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

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Step 2.1

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

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{2}{7} \\ 2 - 2 \cdot 1 & 2 - 2 (\frac{2}{7}) & 7 - 2 (\frac{2}{7}) \end{array}]$

Step 2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{2}{7} \\ 0 & \frac{10}{7} & \frac{45}{7} \end{array}]$

Step 3

Multiply each element of $R_{2}$ by $\frac{7}{10}$ to make the entry at $2, 2$ a $1$ .

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Step 3.1

Multiply each element of $R_{2}$ by $\frac{7}{10}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{2}{7} \\ \frac{7}{10} \cdot 0 & \frac{7}{10} \cdot \frac{10}{7} & \frac{7}{10} \cdot \frac{45}{7} \end{array}]$

Step 3.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{2}{7} & \frac{2}{7} \\ 0 & 1 & \frac{9}{2} \end{array}]$

Step 4

Perform the row operation $R_{1} = R_{1} - \frac{2}{7} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Step 4.1

Perform the row operation $R_{1} = R_{1} - \frac{2}{7} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{2}{7} \cdot 0 & \frac{2}{7} - \frac{2}{7} \cdot 1 & \frac{2}{7} - \frac{2}{7} \cdot \frac{9}{2} \\ 0 & 1 & \frac{9}{2} \end{array}]$

Step 4.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 1 & \frac{9}{2} \end{array}]$

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