Use Gauss-Jordan Elimination to Solve the Linear System and Determine $$\begin{array} { r } x + 3 y + 2 z = 11 \\4 y + 9 z = - 12 \\x + 7 y + 11 z = - 1\end{array}$$

question 56

Multiple Choice

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
- $$\begin{array} { r } x + 3 y + 2 z = 11 \\4 y + 9 z = - 12 \\x + 7 y + 11 z = - 1\end{array}$$

• A) \(\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } + 3 , \mathrm { z } \right)\)
• B) \(\left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right)\)
• C) \(\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } - 3 , \mathrm { z } \right)\)
• D) \(\left( - \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)\)

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Definitions:

Nonverbal Behavior

Communication without the use of spoken language, including gestures, body language, facial expressions, and other forms of physical expression.

Certainty

The state of being sure about something or the absence of doubt.

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A psychological reaction characterized by the need to protect oneself from criticism, perceived threat, or vulnerability, often hindering open communication.

Body Orientation

Body orientation refers to the positioning of an individual’s body, which can communicate attitudes, feelings, or intentions non-verbally in social interactions.