Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { l r r r } 0 & 3 & 0 & - 3 \\4 & 9 & - 3 & - 6 \\8 & 6 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]$$

question 50

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { l r r r } 0 & 3 & 0 & - 3 \\4 & 9 & - 3 & - 6 \\8 & 6 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]$$

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

---

Definitions:

Alcohol Use

The consumption of beverages containing ethanol, which can range from moderate drinking to alcohol abuse and dependence.

Hostility

A state of anger and aggression towards others, often resulting from frustration or perceived threats.

Nicotine

A stimulant compound found in tobacco plants, which is highly addictive and affects the nervous system.

Caffeine

A stimulant found in coffee, tea, and various other plants that can enhance alertness and energy levels.