Question

An eigenvector of the matrix

\[ A= \begin{bmatrix} 3 & 2 \\ 1 & 2 \end{bmatrix} \]

is

• A. \( \begin{bmatrix} 7\\ 2 \end{bmatrix} \)
• B. \( \begin{bmatrix} -2\\ 1 \end{bmatrix} \)
• C. \( \begin{bmatrix} -1\\ 2 \end{bmatrix} \)
• D. \( \begin{bmatrix} 5\\ -5 \end{bmatrix} \)

Hint:

To verify an eigenvector, simply check \[ \boxed{ AX=\lambda X. } \] If the resulting vector is a scalar multiple of the original vector, then it is an eigenvector.

Answer 1

The Correct Option is D