Use a Graphing Calculator and the Method of Matrix Inverses

question 244

Multiple Choice

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
- $$\begin{array} { l } ( \log 2 ) x + ( \ln 3 ) y + ( \ln 5 ) z = 4 \\( \ln 3 ) x + ( \log 8 ) y + ( \ln 10 ) z = 11 \\( \log 23 ) x + ( \ln 7 ) y + ( \ln 4 ) z = 15\end{array}$$

• A) \(\varnothing\)
• B) \(\{ ( 9.25474,1.35236 , - 0.16880 ) \}\)
• C) \(\{ ( 0.30103,9.0309,1.38629 ) \}\)
• D) \(\{ ( 4.12321,3.91519,1.27440 ) \}\)

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Definitions:

Long-Run Supply Curve

A graphical representation that shows how the quantity supplied reacts to price changes in the long-term, accounting for all factors of production adjustments.

Increasing Cost Industry

An industry in which the costs of production increase as the industry's output expands, typically due to resource limitations.

Decreasing-Cost Industry

An industry where the average cost of production decreases as the industry's output increases, often due to economies of scale.

Long-Run Industry Supply Curve

A graphical representation that shows the relationship between the price of a good and the total output of the industry over time, assuming all inputs are variable.