Solve Each System of Equations Using Matrices (Row Operations) $$\begin{array} { l } x + 3 y - 2 z - w = 27 \\4 x + y + z + 2 w = 14 \\- 3 x - y - 3 z - 2 w = - 1 \\x - y - 3 z - 2 w = 11\end{array}$$

question 159

Multiple Choice

Solve each system of equations using matrices (row operations) . If the system has no solution, say that it is inconsistent.
- $$\begin{array} { l } x + 3 y - 2 z - w = 27 \\4 x + y + z + 2 w = 14 \\- 3 x - y - 3 z - 2 w = - 1 \\x - y - 3 z - 2 w = 11\end{array}$$

• A) \(\{ ( 27,14 , - 1,11 ) \}\)
• B) \(\{ ( 3,5 , - 5,1 ) \}\)
• C) \(\{ ( 2,7 , - 9,3 ) \}\)
• D) \(\{ ( 3 + w , 5 - 2 w , - 5 + 2 w , w ) \}\)

---

Definitions:

Center

The point that is equally distant from all points on the circumference of a circle or the surface of a sphere; in geometry, it's the midpoint of any shape or object.

Balancing Point

The point at which an object is in perfect equilibrium under the influence of gravity and does not tip or rotate.

Lever

A rigid bar resting on a pivot point (fulcrum), used to transmit force and movement, exemplifying the principle of mechanical advantage.

Abbreviation

A shortened form of a word or phrase used to save space or provide clarity.