For the Given Matrix A, Find a Basis for the Corresponding

question 2

Multiple Choice

For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue.
- $$A = \left[ \begin{array} { r r r } 1 & 6 & 6 \\6 & 1 & - 6 \\- 6 & 6 & 13\end{array} \right] , \lambda = 7$$

• A)\( \left\{\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right],\left[\begin{array}{r}0 \\ 1 \\ -1\end{array}\right]\right\} \)
• B)\( \left\{\left[\begin{array}{r}1 \\ 0 \\ -1\end{array}\right],\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]\right\} \)
• C)\( \left\{\left[\begin{array}{r}0 \\ 1 \\ -1\end{array}\right]\right\} \)
• D)\( \left\{\left[\begin{array}{r}1 \\ 0 \\ -1\end{array}\right]\right\} \)

Recognize the tools and mechanisms used by the Federal Reserve to influence the money supply and banking operations.

Understand the impact of reserve requirements on the banking system and the overall money supply.

Analyze the role and effects of monetary policy in economic situations, including crisis management.

Understand the concept and implications of bank runs on the financial system and the economy.

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