Find the Inverse, If It Exists, for the Matrix $$A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$$

question 52

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$$

• A)
• \[
• \left[\begin{array}{cccc}
• \frac{1}{2} & -\frac{1}{3} & 0 & \frac{1}{2} \\
• \frac{1}{6} & -\frac{1}{6} & 0 & \frac{1}{4} \\
• \frac{1}{6} & -\frac{1}{12} & 0 & \frac{1}{6} \\
• 0 & 0 & -\frac{1}{2} & 0
• \end{array}\right]
• B)
• \left[\begin{array}{cccc}
• -1 & 1 & 0 & 3 \\
• \frac{1}{2} & 0 & 0 & -\frac{1}{2} \\
• 0 & -\frac{1}{3} & 0 & -\frac{1}{2} \\
• 0 & 0 & -\frac{1}{2} & 0
• \end{array}\right]
• \]
• C)\[
• \left[\begin{array}{cccc}
• -1 & \frac{1}{2} & 0 & 0 \\
• 1 & 0 & -\frac{1}{3} & 0 \\
• 0 & 0 & 0 & -\frac{1}{2} \\
• 3-\frac{1}{2} & -\frac{1}{2} & 0
• \end{array}\right]
• \]
• D) No inverse

---

Definitions:

Marketing Costs

The expenses associated with promoting, selling, and delivering products or services, including advertising, market research, and distribution costs.

Market Share

The percentage of total sales in an industry generated by a particular company, indicating its strength in the market.

Product Line

A group of related products marketed by a single company.

Advertised Alongside

The practice of placing one's advertisements near relevant content or products to attract a targeted audience.