Use Cramer's Rule to Solve the Following System of Linear $$\left\{ \begin{array} { r } 4 x~~~~~ - 8 z = 2 \\- 4 y + 12 z = 3 \\8 x~~~ + 20 z = 0\end{array} \right.$$

question 23

Multiple Choice

Use Cramer's Rule to solve the following system of linear equations: $$\left\{ \begin{array} { r } 4 x~~~~~ - 8 z = 2 \\- 4 y + 12 z = 3 \\8 x~~~ + 20 z = 0\end{array} \right.$$

• A) \(x = \frac { 1 } { 2 } ; y = - \frac { 5 } { 4 } ; z = - \frac { 1 } { 2 }\)
• B) \(x = \frac { 5 } { 18 } ; y = - \frac { 13 } { 12 } ; z = - \frac { 1 } { 9 }\)
• C) \(x = \frac { 1 } { 18 } ; y = - \frac { 13 } { 12 } ; z = - \frac { 1 } { 18 }\)
• D) \(x = \frac { 5 } { 18 } ; y = - \frac { 11 } { 12 } ; z = - \frac { 1 } { 2 }\).
• E) \(x = \frac { 1 } { 2 } ; y = - \frac { 5 } { 4 } ; z = - \frac { 1 } { 2 }\).

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Definitions:

Operations

Activities involved in the day-to-day running of a business for producing and delivering products or services.

Average Time

The mean time taken to complete a task or process, calculated by summing all the recorded times and dividing by the number of observations.

Arrival Rate

The frequency at which entities (e.g., customers, data packets) arrive at a specific point within a system or process.

Poisson Distribution

A distribution of probabilities indicating the likelihood of a certain number of occurrences within a specified time or space interval.