Find the Minor $M _ { 13 }$ And Its Cofactor $C _ { 13 }$

question 50

Multiple Choice

Find the minor $M _ { 13 }$ and its cofactor $C _ { 13 }$ of the matrix $\left[ \begin{array} { c c c } - 9 & 6 & - 24 \\ 9 & - 6 & 18 \\ - 3 & 9 & - 18 \end{array} \right]$

• A) \(M _ { 13 } = \left| \begin{array} { r r } - 9 & - 24 \\ - 3 & - 18 \end{array} \right| = 90\)
• \[C _ { 13 } = - 90\]
• B) \(M _ { 13 } = \left| \begin{array} { c c } 6 & - 24 \\ - 6 & 18 \end{array} \right| = - 36\)
• \[C _ { 13 } = - 36\]
• C) \(M _ { 13 } = \left| \begin{array} { c c } 9 & - 6 \\ - 3 & 9 \end{array} \right| = 63\)
• \[C _ { 13 } = - 63\]
• D)
• \[\begin{array} { l }
• M _ { 13 } = \left| \begin{array} { c c }
• 6 & - 24 \\
• - 6 & 18
• \end{array} \right| = - 36 \\
• C _ { 13 } = 36
• \end{array}\]
• E)
• \[\begin{array} { l }
• M _ { 13 } = \left| \begin{array} { c c }
• 9 & - 6 \\
• - 3 & 9
• \end{array} \right| = 63 \\
• C _ { 13 } = 63
• \end{array}\]

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Definitions:

Equity Multiplier

A ratio of financial leverage which quantifies the fraction of a company's assets funded by the equity of its shareholders.

Net Profit Margin

A financial ratio that shows the percentage of net income to revenue, indicating the efficiency at which a company converts sales into net profit.

Gross Margin

The difference between the sales revenue and the cost of goods sold, indicating the profitability of a company's core business activities.

Times Interest Earned

A financial ratio that measures a company's ability to meet its debt obligations based on its earnings before interest and taxes (EBIT).