Use the Row Reduction Method to Find the Inverse of the Matrix

question 76

Multiple Choice

Use the row reduction method to find the inverse of the matrix, if it exists. $A = \left[ \begin{array} { c c c } 1 & 3 & 0 \\- 1 & 3 & 0 \\3 & 0 & 2\end{array} \right]$

• A) \(\left[ \begin{array} { c c c }
• \frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\
• - \frac { 3 } { 4 } & \frac { 3 } { 4 } & \frac { 1 } { 2 } \\
• \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c c }
• \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0 \\
• \frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\
• - \frac { 3 } { 4 } & \frac { 3 } { 4 } & \frac { 1 } { 2 }
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c c }
• \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0 \\
• \frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\
• \frac { 3 } { 4 } & - \frac { 3 } { 4 } & \frac { 1 } { 2 }
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c }
• \frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\
• \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0 \\
• - \frac { 3 } { 4 } & \frac { 3 } { 4 } & \frac { 1 } { 2 }
• \end{array} \right]\)
• E) The inverse matrix does not exist.

---

Definitions:

Nonsystematic Variance

The portion of an asset's total variance that is attributable to factors unique to that specific asset, as opposed to broader market influences.

Market Index

A metric that measures the performance of a basket of securities intended to represent a particular market or segment of it, like the S&P 500 or NASDAQ.

Treynor-Black Model

A portfolio optimization model that integrates market equilibrium theory with security selection to enhance portfolio performance.

Nonsystematic Risk

The risk associated with an individual asset or company, which can be reduced through diversification, unlike systematic risk.