Find All Solutions of the System $$\left\{ \begin{array} { l } x + y + z + w = 4 \\x - 2 y - z - w = 6 \\2 x - y + z - w = 5 \\x - y + 2 z - 2 w = - 5\end{array} \right.$$

question 5

Multiple Choice

Find all solutions of the system. $$\left\{ \begin{array} { l } x + y + z + w = 4 \\x - 2 y - z - w = 6 \\2 x - y + z - w = 5 \\x - y + 2 z - 2 w = - 5\end{array} \right.$$

• A) \(( 0 , - 2,4,5 )\)
• B) \(( 5,0 , - 3,2 )\)
• C) \(( - 8,2 , - 5,0 )\)
• D) \(\text { The system is dependent. }\)
• E) \(\text { The system is inconsistent. }\)

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Definitions:

Proprioceptor

Class of mechanoreceptor responsible for maintaining the body’s equilibrium and posture; involved in reflex actions.

Organ of Corti

The sensory organ located within the cochlea of the inner ear, responsible for converting sound vibrations into nerve impulses.

Retina

A layer at the back of the eyeball containing cells sensitive to light, which trigger nerve impulses that pass via the optic nerve to the brain.

Rods and Cones

Photoreceptor cells in the retina of the eye where rods are responsible for vision at low light levels, and cones handle color vision and detail.