Use Cramer S Rule to Find the Solution Set for the System

question 49

Short Answer

Use Cramer s rule to find the solution set for the system. $$\left( \begin{array} { r l } 4 x - y + 5 z & = 31 \\5 y + z & = 23 \\x - 4 y - z & = - 14\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

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Definitions:

Intuitive

Pertaining to using or based on what one feels to be true even without conscious reasoning; instinctive.

Programmed Decisions

Decision-making processes that are routine and repetitive, often automated or guided by established policies and procedures.

"If-then" Decision Rules

Logical constructs used in decision-making that trigger specific actions if certain conditions are met.

Framing Error

A cognitive bias where information is perceived and interpreted through a subjective lens, potentially leading to misconceptions.