Algebra Examples

$[\begin{array}{c} 2 & - 4 & | 9 | \\ 3 & - 7 & | - 9 | \end{array}]$

Step 1

The absolute value is the distance between a number and zero. The distance between $0$ and $9$ is $9$ .

$[\begin{array}{c} 2 & - 4 & 9 \\ 3 & - 7 & | - 9 | \end{array}]$

Step 2

The absolute value is the distance between a number and zero. The distance between $- 9$ and $0$ is $9$ .

$[\begin{array}{c} 2 & - 4 & 9 \\ 3 & - 7 & 9 \end{array}]$

Step 3

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

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Step 3.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{- 4}{2} & \frac{9}{2} \\ 3 & - 7 & 9 \end{array}]$

Step 3.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & - 2 & \frac{9}{2} \\ 3 & - 7 & 9 \end{array}]$

Step 4

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

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Step 4.1

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

$[\begin{array}{c} 1 & - 2 & \frac{9}{2} \\ 3 - 3 \cdot 1 & - 7 - 3 \cdot - 2 & 9 - 3 (\frac{9}{2}) \end{array}]$

Step 4.2

Simplify $R_{2}$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Simplify $R_{2}$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & \frac{27}{2} \\ 0 & 1 & \frac{9}{2} \end{array}]$