Solve the System of Equations $\left\{ \begin{array} { r } x + 3 y - 2 z = 1 \\2 x + 4 y + z = 4 \\2 x + 6 y - z = 2\end{array} \right.$

question 3

Multiple Choice

Solve the system of equations $\left\{ \begin{array} { r } x + 3 y - 2 z = 1 \\2 x + 4 y + z = 4 \\2 x + 6 y - z = 2\end{array} \right.$ by converting to a matrix equation and using its inverse coefficient matrix $\left[ \begin{array} { c c c } \frac { 3 } { 3 } & \frac { 3 } { 2 } & - \frac { 11 } { 6 } \\- \frac { 2 } { 3 } & - \frac { 1 } { 2 } & \frac { 3 } { 6 } \\- \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 }\end{array} \right]$

• A) \(( - 14 , - 3,0 )\)
• B) \(( 2,3,0 )\)
• C) \(( - 8,3,0 )\)
• D) \(( - 8,0,1 )\)
• E) \(( - 6 , - 3,0 )\)

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Definitions:

Member Satisfaction

The level of contentment or fulfilment experienced by individuals within a group or organization, often considered a key factor in group dynamics and outcomes.

Group Performance

Group performance encompasses the outcome or output produced by a group, measured against set goals or standards.

SYMLOG Theory

A theoretical framework in social psychology that stands for SYstem for the Multiple Level Observation of Groups, focusing on the observation and analysis of the behavior of individuals within groups in three dimensions: dominance/submission, friendliness/unfriendliness, and instrumentally controlled/emotionally expressive.

Character Structure

A concept in psychology that refers to the organization and dynamic interplay of traits, values, and patterns of behavior that make up an individual's personality.