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:

Aggressive Behavior

Actions intended to harm or intimidate others, often stemming from frustration, anger, or attempts to assert dominance.

Hostile Behavior

Actions or attitudes that are aggressive, unfriendly, or antagonistic towards others.

Blasting Intense Noise

The act of emitting extremely loud and potentially damaging sound, often used as a form of crowd control or psychological manipulation.

Mere Exposure Effect

The psychological phenomenon by which people tend to develop a preference for things merely because they are familiar with them.