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 $\left[ \begin{array} { c c c c } \frac { 5 } { 2 } & \frac { 1 } { 2 } & 0 & - 2 \\- 1 & 0 & 0 & 1 \\- \frac { 1 } { 2 } & - \frac { 1 } { 2 } & - 1 & 2 \\1 & 0 & 1 & - 2\end{array} \right]$ .

---

Definitions:

Denominator

The bottom number in a fraction, which represents the total number of equal parts the whole is divided into.

Metric Units

A system of measurement based on powers of ten, including units such as meters, liters, and grams.

Volume

The amount of space occupied by an object as measured in cubic units.

Improper Fraction

A fraction in which the top number is greater than or equal to the bottom number.