Write the System of Linear Equations Represented by the Augmented $\left[ \begin{array} { r r r | r } 6 & 5 & 3 & - 2 \\ 2 & 0 & 7 & 4 \\ 4 & 2 & 0 & 2 \end{array} \right]$

question 61

Multiple Choice

Write the system of linear equations represented by the augmented matrix. Use x, y, z, and, if necessary, w for the variables.
- $\left[ \begin{array} { r r r | r } 6 & 5 & 3 & - 2 \\ 2 & 0 & 7 & 4 \\ 4 & 2 & 0 & 2 \end{array} \right]$

• A) \(6 x + 5 y + 3 z = - 2\)
• \(2 x + 7 z = 4\)
• \(4 x + 2 y = 2\)
• B) \(6 x - 5 y + 3 z = - 2\)
• \(2 x + 7 z = - 4\)
• \(4 x + 2 y = - 2\)
• C) \(6 x + 5 y + 3 z = - 2\)
• \(2 x + 7 z = 4\)
• \(4 x + 2 z = 2\)
• D) \(6 x + 5 y + 3 z = - 2\)
• \(2 x + y + 7 z = 4\)

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Definitions:

Economies of Scale

The cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output generally decreasing with increasing scale as fixed costs are spread out over more units of output.

Long-run Average Total Costs

The average cost per unit of output where all inputs, including capital, are variable and the firm has adjusted all inputs to find the lowest average cost.

Long-run Marginal Cost

The change in total cost when producing one additional unit of a product or service in the long term, where all inputs are considered variable.

Economies of Scale

Enterprises gain cost benefits from their operation size, as the cost for each unit produced typically drops when the scale enlarges because fixed expenses are distributed across a greater number of output units.