Write the System of Equations in Matrix Form $$\left\{ \begin{array} { l } a - b + c = 8 \\4 a - b + c = 0 \\a + b + 2 c = 7 \\a + c + d = 0\end{array} \right.$$

question 9

Multiple Choice

Write the system of equations in matrix form. $$\left\{ \begin{array} { l } a - b + c = 8 \\4 a - b + c = 0 \\a + b + 2 c = 7 \\a + c + d = 0\end{array} \right.$$

• A) \(\left[ \begin{array} { c c c c }
• 1 & - 1 & 1 & 0 \\
• 4 & - 1 & 1 & 0 \\
• 1 & 1 & 2 & 0 \\
• 1 & 0 & 1 & 1
• \end{array} \right] \left[ \begin{array} { l }
• a \\
• b \\
• c \\
• a
• \end{array} \right] = \left[ \begin{array} { l }
• 8 \\
• 0 \\
• 7 \\
• 0
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c c c }
• 8 & - 1 & 1 & 0 \\
• 0 & - 1 & 1 & 0 \\
• 7 & 1 & 2 & 0 \\
• 0 & 0 & 1 & 1
• \end{array} \right] \left[ \begin{array} { l }
• a \\
• b \\
• c \\
• a
• \end{array} \right] = \left[ \begin{array} { l }
• 1 \\
• 4 \\
• 1 \\
• 1
• \end{array} \right]\)
• C) \(\left[ \begin{array} { l l l l }
• 8 & 1 & 1 & 0 \\
• 0 & 4 & 1 & 0 \\
• 7 & 1 & 2 & 0 \\
• 0 & 1 & 1 & 1
• \end{array} \right] \left[ \begin{array} { l }
• a \\
• b \\
• c \\
• a
• \end{array} \right] = \left[ \begin{array} { l }
• 0 \\
• 0 \\
• 0 \\
• 1
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c }
• 1 & - 1 & 1 \\
• 4 & - 1 & 1 \\
• 1 & 1 & 2
• \end{array} \right] \left[ \begin{array} { l }
• a \\
• b \\
• c
• \end{array} \right] = \left[ \begin{array} { l }
• 8 \\
• 0 \\
• 7
• \end{array} \right]\)
• E) none

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Definitions:

Opportunity Cost Curve

A graphical representation that shows the trade-offs between two options, highlighting what is sacrificed when choosing one option over another.

Excess Capacity

A situation where a firm operates below its maximum production capacity, indicating it can increase output without incurring higher fixed costs.

Variable Costs

Expenses that change in proportion to the level of goods or services produced, such as materials and labor costs.

Repeat Customers

Customers who return to a business to make subsequent purchases, showing loyalty and continued interest in a company's products or services.