Algebra Examples

$[\begin{array}{c} - 6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \end{array}]$

Step 1

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

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Step 1.1

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

$[\begin{array}{c} - \frac{1}{6} \cdot - 6 & - \frac{1}{6} \cdot 8 & - \frac{1}{6} \cdot 0 & - \frac{1}{6} \cdot 0 \\ 4 & 1 & 9 & 2 \end{array}]$

Step 1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ 4 & 1 & 9 & 2 \end{array}]$

Step 2

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Step 2.1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ 4 - 4 \cdot 1 & 1 - 4 (- \frac{4}{3}) & 9 - 4 \cdot 0 & 2 - 4 \cdot 0 \end{array}]$

Step 2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ 0 & \frac{19}{3} & 9 & 2 \end{array}]$

Step 3

Multiply each element of $R_{2}$ by $\frac{3}{19}$ to make the entry at $2, 2$ a $1$ .

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Step 3.1

Multiply each element of $R_{2}$ by $\frac{3}{19}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ \frac{3}{19} \cdot 0 & \frac{3}{19} \cdot \frac{19}{3} & \frac{3}{19} \cdot 9 & \frac{3}{19} \cdot 2 \end{array}]$

Step 3.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & 0 & 0 \\ 0 & 1 & \frac{27}{19} & \frac{6}{19} \end{array}]$

Step 4

Perform the row operation $R_{1} = R_{1} + \frac{4}{3} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Step 4.1

Perform the row operation $R_{1} = R_{1} + \frac{4}{3} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + \frac{4}{3} \cdot 0 & - \frac{4}{3} + \frac{4}{3} \cdot 1 & 0 + \frac{4}{3} \cdot \frac{27}{19} & 0 + \frac{4}{3} \cdot \frac{6}{19} \\ 0 & 1 & \frac{27}{19} & \frac{6}{19} \end{array}]$

Step 4.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & \frac{36}{19} & \frac{8}{19} \\ 0 & 1 & \frac{27}{19} & \frac{6}{19} \end{array}]$