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)\( \left\{\left[\begin{array}{r}1 \\ 0 \\ -1\end{array}\right]\right\} \)

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Definitions:

Minimizing Resistance

Refers to strategies and efforts made to reduce opposition or reluctance towards change within an organization or individual.

Coaching

A developmental process where an individual, usually more experienced, supports and guides another individual to achieve specific personal or professional goals.

Force Field Analysis

A management technique developed by Kurt Lewin, used to identify and analyze the forces that affect change within an organization.

Unfreezing

The process of making individuals more open to change by overcoming inertia and dismantling existing mindsets.