Finite Math Examples

$[\begin{array}{c} 0.4 & 0 & 0.2 & 17800 \\ 0.3 & 0.5 & 0.3 & 28600 \\ 0.3 & 0.5 & 0.5 & 39600 \end{array}]$

Step 1

Multiply each element of $R_{1}$ by $\frac{1}{0.4}$ to make the entry at $1, 1$ a $1$ .

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Step 1.1

Multiply each element of $R_{1}$ by $\frac{1}{0.4}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{0.4}{0.4} & \frac{0}{0.4} & \frac{0.2}{0.4} & \frac{17800}{0.4} \\ 0.3 & 0.5 & 0.3 & 28600 \\ 0.3 & 0.5 & 0.5 & 39600 \end{array}]$

Step 1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0.3 & 0.5 & 0.3 & 28600 \\ 0.3 & 0.5 & 0.5 & 39600 \end{array}]$

Step 2

Perform the row operation $R_{2} = R_{2} - 0.3 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Step 2.1

Perform the row operation $R_{2} = R_{2} - 0.3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0.3 - 0.3 \cdot 1 & 0.5 - 0.3 \cdot 0 & 0.3 - 0.3 \cdot 0.5 & 28600 - 0.3 \cdot 44500 \\ 0.3 & 0.5 & 0.5 & 39600 \end{array}]$

Step 2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 0.5 & 0.15 & 15250 \\ 0.3 & 0.5 & 0.5 & 39600 \end{array}]$

Step 3

Perform the row operation $R_{3} = R_{3} - 0.3 R_{1}$ to make the entry at $3, 1$ a $0$ .

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Step 3.1

Perform the row operation $R_{3} = R_{3} - 0.3 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 0.5 & 0.15 & 15250 \\ 0.3 - 0.3 \cdot 1 & 0.5 - 0.3 \cdot 0 & 0.5 - 0.3 \cdot 0.5 & 39600 - 0.3 \cdot 44500 \end{array}]$

Step 3.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 0.5 & 0.15 & 15250 \\ 0 & 0.5 & 0.35 & 26250 \end{array}]$

Step 4

Multiply each element of $R_{2}$ by $\frac{1}{0.5}$ to make the entry at $2, 2$ a $1$ .

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Step 4.1

Multiply each element of $R_{2}$ by $\frac{1}{0.5}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ \frac{0}{0.5} & \frac{0.5}{0.5} & \frac{0.15}{0.5} & \frac{15250}{0.5} \\ 0 & 0.5 & 0.35 & 26250 \end{array}]$

Step 4.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 1 & 0.3 & 30500 \\ 0 & 0.5 & 0.35 & 26250 \end{array}]$

Step 5

Perform the row operation $R_{3} = R_{3} - 0.5 R_{2}$ to make the entry at $3, 2$ a $0$ .

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Step 5.1

Perform the row operation $R_{3} = R_{3} - 0.5 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 1 & 0.3 & 30500 \\ 0 - 0.5 \cdot 0 & 0.5 - 0.5 \cdot 1 & 0.35 - 0.5 \cdot 0.3 & 26250 - 0.5 \cdot 30500 \end{array}]$

Step 5.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 1 & 0.3 & 30500 \\ 0 & 0 & 0.2 & 11000 \end{array}]$

Step 6

Multiply each element of $R_{3}$ by $\frac{1}{0.2}$ to make the entry at $3, 3$ a $1$ .

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Step 6.1

Multiply each element of $R_{3}$ by $\frac{1}{0.2}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 1 & 0.3 & 30500 \\ \frac{0}{0.2} & \frac{0}{0.2} & \frac{0.2}{0.2} & \frac{11000}{0.2} \end{array}]$

Step 6.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 1 & 0.3 & 30500 \\ 0 & 0 & 1 & 55000 \end{array}]$

Step 7

Perform the row operation $R_{2} = R_{2} - 0.3 R_{3}$ to make the entry at $2, 3$ a $0$ .

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Step 7.1

Perform the row operation $R_{2} = R_{2} - 0.3 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 - 0.3 \cdot 0 & 1 - 0.3 \cdot 0 & 0.3 - 0.3 \cdot 1 & 30500 - 0.3 \cdot 55000 \\ 0 & 0 & 1 & 55000 \end{array}]$

Step 7.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44500 \\ 0 & 1 & 0 & 14000 \\ 0 & 0 & 1 & 55000 \end{array}]$

Step 8

Perform the row operation $R_{1} = R_{1} - 0.5 R_{3}$ to make the entry at $1, 3$ a $0$ .

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Step 8.1

Perform the row operation $R_{1} = R_{1} - 0.5 R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 0.5 \cdot 0 & 0 - 0.5 \cdot 0 & 0.5 - 0.5 \cdot 1 & 44500 - 0.5 \cdot 55000 \\ 0 & 1 & 0 & 14000 \\ 0 & 0 & 1 & 55000 \end{array}]$

Step 8.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 17000 \\ 0 & 1 & 0 & 14000 \\ 0 & 0 & 1 & 55000 \end{array}]$