Find the Characteristic Equation of the Given Matrix $$A = \left[ \begin{array} { r r r r } 8 & - 1 & 5 & 2 \\0 & 3 & 1 & - 1 \\0 & 0 & - 6 & - 6 \\0 & 0 & 0 & - 5\end{array} \right]$$

question 9

Multiple Choice

Find the characteristic equation of the given matrix.
- $$A = \left[ \begin{array} { r r r r } 8 & - 1 & 5 & 2 \\0 & 3 & 1 & - 1 \\0 & 0 & - 6 & - 6 \\0 & 0 & 0 & - 5\end{array} \right]$$

• A) \(( 8 - \lambda ) ( 3 - \lambda ) ( - 6 - \lambda ) ( - 5 - \lambda ) = 0\)
• B) \(( 8 - \lambda ) ( - 1 - \lambda ) ( 5 - \lambda ) ( 2 - \lambda ) = 0\)
• C) \(( - 5 - \lambda ) ( - 6 - \lambda ) ( - 1 - \lambda ) ( 2 - \lambda ) = 0\)
• D) \(( 2 - \lambda ) ( - 1 - \lambda ) ( - 6 - \lambda ) ( - 5 - \lambda ) = 0\)

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Definitions:

Trading Range

The difference between the highest and the lowest prices at which a security trades over a certain period of time.

Repurchase Range

The price range within which a company intends to buy back its own shares from the market, often to reduce the overall share count and increase shareholder value.

Target Payout Range

The designated percentage range of net income that a company aims to distribute to its shareholders as dividends.

Preferred Trading Range

The price range within which a security is considered attractive for purchase or sale by investors based on historical price movements and other factors.