Use Cramer's Rule to Find the Solution of the System $$\left\{ \begin{array} { c } x - y - z = 1 \\x + y + z = 19 \\- x - y + z = - 11\end{array} \right.$$

question 46

Multiple Choice

Use Cramer's rule to find the solution of the system, if possible. $$\left\{ \begin{array} { c } x - y - z = 1 \\x + y + z = 19 \\- x - y + z = - 11\end{array} \right.$$

• A) \(x = 10 , y = 5 , z = 4\)
• B) \(x = 5 , y = 10 , z = 4\)
• C) \(x = 4 , y = 5 , z = 10\)
• D) The system is inconsistent.
• E) The equations are dependent.

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Definitions:

Perceptual Constancy

The brain's ability to recognize objects as unchanging even as illumination and retinal images change in shape, size, or color.

Movement Parallax

Movement parallax is a depth cue that arises because objects at different distances move across the visual field at different rates relative to the observer’s motion.

Good Continuation

A principle in Gestalt psychology suggesting that elements aligned in a particular direction are perceived as a more unified whole.

Gestalt Law

Principles of perception that suggest humans naturally perceive objects as organized patterns and wholes rather than as separate components.