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 51

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:

Third-force Perspective

A psychological framework that emphasizes human potential and self-actualization, often associated with humanistic psychology.

Human Potential

The inherent ability or capacity for growth, development, and achievement present within each person.

Self-realization

The process of fully understanding and realizing one's own potential, abilities, or character.

Self-determination

The process by which a person controls their own life and makes decisions independently, often linked to motivation and personal growth.