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 39

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:

Five-factor Model

A framework identifying five major dimensions of human personality: openness, conscientiousness, extraversion, agreeableness, and neuroticism.

Agreeableness

A personality trait characterized by warmth, kindness, and a willingness to cooperate and avoid conflict.

Neuroticism

A personality trait characterized by moodiness, anxiety, and emotional instability.

Social Desirability

The behavior of those answering questions to do so in a manner they assume will generate favorable opinions from others.