The Matrix Is the Reduced Echelon Matrix for a System $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 10 & - 8 \\0 & 1 & 0 & 0 & 5 \\0 & 0 & 1 & 6 & 3 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

question 83

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. $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 10 & - 8 \\0 & 1 & 0 & 0 & 5 \\0 & 0 & 1 & 6 & 3 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

• A) ( \(-\) 8 \(-\) 10 k , 5, 3 \(-\) 6 k , k ), where k is any real number
• B) ( \(-\) 8 \(-\) 10 k , 5, 3 + 6 k , k ), where k is any real number
• C) ( \(-\) 8 + 10 k , 5, 3 \(-\) 6 k , k ), where k is any real number
• D) ( \(-\) 8 + 10 k , 5, 3 + 6 k , k ), where k is any real number
• E) inconsistent

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Definitions:

Affirming The Consequent

An invalid mixed hypothetical syllogism in which the categorical premise affirms the consequent of the hypothetical premise and the conclusion affirms the antecedent.

Explanandum

The phenomenon or event that is to be explained in a scientific or philosophical inquiry.

Hypothesis

A proposed explanation for a phenomenon made as a starting point for further investigation, testing, or experimentation.

Plausible

Seeming reasonable or probable; believable or credible.