Algebra Examples

$[\begin{array}{c} 0 & 1 & 2 & 3 \\ 6 & 18 & 54 & 162 \end{array}]$

Step 1

Swap $R_{2}$ with $R_{1}$ to put a nonzero entry at $1, 1$ .

$[\begin{array}{c} 6 & 18 & 54 & 162 \\ 0 & 1 & 2 & 3 \end{array}]$

Step 2

Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

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Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{1}{6} \cdot 6 & \frac{1}{6} \cdot 18 & \frac{1}{6} \cdot 54 & \frac{1}{6} \cdot 162 \\ 0 & 1 & 2 & 3 \end{array}]$

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 3 & 9 & 27 \\ 0 & 1 & 2 & 3 \end{array}]$

Step 3

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

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

$[\begin{array}{c} 1 - 3 \cdot 0 & 3 - 3 \cdot 1 & 9 - 3 \cdot 2 & 27 - 3 \cdot 3 \\ 0 & 1 & 2 & 3 \end{array}]$

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 3 & 18 \\ 0 & 1 & 2 & 3 \end{array}]$