Find the Complete Solution of the Linear System or Show $$\left\{ \begin{array} { r } x + 2 y + z + w = 0 \\x + 2 y - z - w = 0 \\x + 4 y + z + 2 w = - 1 \\x + 3 y + z + w = 2\end{array} \right.$$

question 135

Essay

Find the complete solution of the linear system or show that it is inconsistent. $$\left\{ \begin{array} { r } x + 2 y + z + w = 0 \\x + 2 y - z - w = 0 \\x + 4 y + z + 2 w = - 1 \\x + 3 y + z + w = 2\end{array} \right.$$

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Definitions:

Dialectical Behavior Therapy

A comprehensive cognitive-behavioral treatment that emphasizes individual psychotherapy and group skills training classes to help people manage emotional instability and interpersonal difficulties.

Self-mutilation

The intentional act of harming one's own body as a way to cope with emotional pain, stress, or psychological disorders.

Limit Setting

The process of establishing boundaries or rules to manage behavior, commonly used in therapy and parenting.

Provocative

Describes actions or behaviors intended to elicit a strong reaction or emotion, often deliberately challenging or controversial.