Use Cramer's Rule to Solve the System $$\left\{ \begin{aligned}6 x + 4 y - 2 z = & 10 \\2 x - 3 y + 4 z = & 4 \\15 x - 18 z = & - 21\end{aligned} \right.$$

question 7

Multiple Choice

Use Cramer's rule to solve the system. $$\left\{ \begin{aligned}6 x + 4 y - 2 z = & 10 \\2 x - 3 y + 4 z = & 4 \\15 x - 18 z = & - 21\end{aligned} \right.$$

• A) \(( 2,1,1 )\)
• B) \(( 1,0,2 )\)
• C) \(( 1,2,1 )\)
• D) \(( 1,2,2 )\)
• E) \(\text { The system is inconsistent. }\)

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Definitions:

Statistical Power

Statistical power refers to the probability that a statistical test will correctly reject a false null hypothesis, effectively detecting an effect when there is one.

Detecting An Effect

The process of identifying whether a particular treatment, condition, or variable has a statistically significant impact in an experiment or study.

Type I Error

The error made in statistical hypothesis testing when a true null hypothesis is incorrectly rejected, commonly referred to as a "false positive."

Type I Error

Type I error, often denoted as α, occurs when a true null hypothesis is incorrectly rejected, indicating a false positive finding in hypothesis testing.