Finite Math Examples

$[\begin{array}{c} 0.4 & 0 & 0.2 & 17600 \\ 0.4 & 0.5 & 0.3 & 29800 \\ 0.2 & 0.5 & 0.5 & 36600 \end{array}]$

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 $1$ .

$[\begin{array}{c} \frac{0.4}{0.4} & \frac{0}{0.4} & \frac{0.2}{0.4} & \frac{17600}{0.4} \\ 0.4 & 0.5 & 0.3 & 29800 \\ 0.2 & 0.5 & 0.5 & 36600 \end{array}]$

Step 1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0.4 & 0.5 & 0.3 & 29800 \\ 0.2 & 0.5 & 0.5 & 36600 \end{array}]$

Step 2

Perform the row operation $R_{2} = R_{2} - 0.4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Step 2.1

Perform the row operation $R_{2} = R_{2} - 0.4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0.4 - 0.4 \cdot 1 & 0.5 - 0.4 \cdot 0 & 0.3 - 0.4 \cdot 0.5 & 29800 - 0.4 \cdot 44000 \\ 0.2 & 0.5 & 0.5 & 36600 \end{array}]$

Step 2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 0.5 & 0.1 & 12200 \\ 0.2 & 0.5 & 0.5 & 36600 \end{array}]$

Step 3

Perform the row operation $R_{3} = R_{3} - 0.2 R_{1}$ to make the entry at $3, 1$ a $0$ .

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Step 3.1

Perform the row operation $R_{3} = R_{3} - 0.2 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 0.5 & 0.1 & 12200 \\ 0.2 - 0.2 \cdot 1 & 0.5 - 0.2 \cdot 0 & 0.5 - 0.2 \cdot 0.5 & 36600 - 0.2 \cdot 44000 \end{array}]$

Step 3.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 0.5 & 0.1 & 12200 \\ 0 & 0.5 & 0.4 & 27800 \end{array}]$

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 $1$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ \frac{0}{0.5} & \frac{0.5}{0.5} & \frac{0.1}{0.5} & \frac{12200}{0.5} \\ 0 & 0.5 & 0.4 & 27800 \end{array}]$

Step 4.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 1 & 0.2 & 24400 \\ 0 & 0.5 & 0.4 & 27800 \end{array}]$

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 $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 1 & 0.2 & 24400 \\ 0 - 0.5 \cdot 0 & 0.5 - 0.5 \cdot 1 & 0.4 - 0.5 \cdot 0.2 & 27800 - 0.5 \cdot 24400 \end{array}]$

Step 5.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 1 & 0.2 & 24400 \\ 0 & 0 & 0.3 & 15600 \end{array}]$

Step 6

Multiply each element of $R_{3}$ by $\frac{1}{0.3}$ to make the entry at $3, 3$ a $1$ .

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Step 6.1

Multiply each element of $R_{3}$ by $\frac{1}{0.3}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 1 & 0.2 & 24400 \\ \frac{0}{0.3} & \frac{0}{0.3} & \frac{0.3}{0.3} & \frac{15600}{0.3} \end{array}]$

Step 6.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 1 & 0.2 & 24400 \\ 0 & 0 & 1 & 52000 \end{array}]$

Step 7

Perform the row operation $R_{2} = R_{2} - 0.2 R_{3}$ to make the entry at $2, 3$ a $0$ .

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Step 7.1

Perform the row operation $R_{2} = R_{2} - 0.2 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 - 0.2 \cdot 0 & 1 - 0.2 \cdot 0 & 0.2 - 0.2 \cdot 1 & 24400 - 0.2 \cdot 52000 \\ 0 & 0 & 1 & 52000 \end{array}]$

Step 7.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 0.5 & 44000 \\ 0 & 1 & 0 & 14000 \\ 0 & 0 & 1 & 52000 \end{array}]$

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 $0$ .

$[\begin{array}{c} 1 - 0.5 \cdot 0 & 0 - 0.5 \cdot 0 & 0.5 - 0.5 \cdot 1 & 44000 - 0.5 \cdot 52000 \\ 0 & 1 & 0 & 14000 \\ 0 & 0 & 1 & 52000 \end{array}]$

Step 8.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 18000 \\ 0 & 1 & 0 & 14000 \\ 0 & 0 & 1 & 52000 \end{array}]$