Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$$

question 14

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$$

• A) The inverse does not exist.
• B)
• \[\left[ \begin{array} { c c c }
• 1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \\
• 1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \\
• \frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 }
• \end{array} \right]\]
• C)
• \[\left[ \begin{array} { r r r }
• - 3 & 10 & - 3 \\
• 2 & - 4 & 1 \\
• - 1 & 1 & 0
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { l l l }
• - 1 & - 3 & - 2 \\
• - 1 & - 3 & - 3 \\
• - 2 & - 7 & - 8
• \end{array} \right]\]

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Definitions:

Brainstem

The posterior part of the brain, adjoining and structurally continuous with the spinal cord, responsible for vital life functions such as breathing, heart rate, and blood pressure.

Midbrain

An area of the brainstem involved in vision, hearing, motor control, sleep/wake, arousal (alertness), and temperature regulation.

Caffeine

A stimulant of the central nervous system found in coffee, tea, chocolate, and various medications, known for its ability to reduce fatigue and improve concentration.

Nicotine

A stimulant and potent parasympathomimetic alkaloid that is naturally produced in the nightshade family of plants and is widely used for its stimulating and relaxing effects.