The Matrix Is the Reduced Echelon Matrix for a System $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & - 8 \\0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & - 9\end{array} \right]$$

question 103

Multiple Choice

The matrix is the reduced echelon matrix for a system with variables x 1 , x 2 , x 3 , and x 4 . Find the solution set of the system. $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & - 8 \\0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & - 9\end{array} \right]$$

• A) ( \(-\) 3, \(-\) 10, 2, \(-\) 12)
• B) (0, \(-\) 10, 0, \(-\) 12)
• C) (3, \(-\) 8, \(-\) 2, \(-\) 9)
• D) (0, \(-\) 8, 0, \(-\) 9)
• E) inconsistent

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Definitions:

Boole's Inequality

A mathematical theorem that describes the upper bound on the probability of the union of several events, emphasizing the limitations of additive probabilities.

Hindsight Bias

The tendency to believe, after learning an outcome, that one would have foreseen it, often referred to as the "I-knew-it-all-along" phenomenon.

Overconfidence Bias

A cognitive bias which leads an individual to overestimate their knowledge, abilities, or control over situations.

Selection Bias

A type of bias caused by choosing non-random data for statistical analysis, which can cause the results to not be representative of the whole population.