Use the Gauss-Jordan Method to Solve the System of Equations $$\begin{aligned}7 x - 9 y - z & = - 24 \\x - 3 y - 5 z & = - 54 \\- 2 x + y + z & = 7\end{aligned}$$

question 145

Multiple Choice

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last
variable be the arbitrary variable.
- $$\begin{aligned}7 x - 9 y - z & = - 24 \\x - 3 y - 5 z & = - 54 \\- 2 x + y + z & = 7\end{aligned}$$

• A) \(\{ ( 3,9,4 ) \}\)
• B) \(\{ ( 3,4,9 ) \}\)
• C) \(\varnothing\)
• D) \(\{ ( - 3,4,6 ) \}\)

Understand the concept of price being driven to minimum average total cost in competitive markets due to characteristics like free entry and exit.

Analyze how changes in a firm's output level affect its profitability in a competitive market.

Recognize the implications of a firm producing at a level where marginal cost exceeds or is less than marginal revenue.

Understand the impact of market conditions on a firm's decision to adjust output rather than price in a competitive price-taker market.

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