Find the Complete Solution of the Linear System or Show $\left\{ \begin{array} { r } 2 x + 2 y - 2 z = 0 \\x + y + 2 z = - 1 \\x + y - z = 2\end{array} \right.$

question 105

Essay

Find the complete solution of the linear system or show that it is inconsistent. $\left\{ \begin{array} { r } 2 x + 2 y - 2 z = 0 \\x + y + 2 z = - 1 \\x + y - z = 2\end{array} \right.$

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Definitions:

Task-Oriented Behavior

A leadership approach focused primarily on the completion of tasks and the achievement of objectives.

Initiating Structure

The act of defining roles, assigning tasks, and establishing clear patterns of organization and communication within a team or organization.

Maintenance Behavior

Actions or activities aimed at preserving the current state of a system, organization, or relationship, ensuring its continuous operation and effectiveness.

Task-Oriented Behavior

Focuses on assigning tasks, clarifying responsibilities, and ensuring the team achieves its goals efficiently.