Solve the System of Equations $\left\{ \begin{array} { r } x + 2 y + z + w = 0 \\x + 2 y - z - w = 0 \\x + 4 y + z + 2 w = - 1 \\x + 3 y + z + w = 2\end{array} \right.$

question 11

Essay

Solve the system of equations $\left\{ \begin{array} { r } x + 2 y + z + w = 0 \\x + 2 y - z - w = 0 \\x + 4 y + z + 2 w = - 1 \\x + 3 y + z + w = 2\end{array} \right.$ by converting to a matrix equation and using its inverse coefficient matrix $\left[ \begin{array} { c c c c } \frac { 5 } { 2 } & \frac { 1 } { 2 } & 0 & - 2 \\- 1 & 0 & 0 & 1 \\- \frac { 1 } { 2 } & - \frac { 1 } { 2 } & - 1 & 2 \\1 & 0 & 1 & - 2\end{array} \right]$ .

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Raw Materials

Basic materials extracted from the environment or farmed, which are used in the initial stages of the production process.

Ethical Concerns

Issues pertaining to the principles of right and wrong behavior, particularly regarding conduct in professional and business contexts.

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The release of harmful substances and pollutants into the environment as a result of industrial activities, leading to environmental degradation and health risks.