Question

Find the eigenvalues of the matrix: \[ A = \begin{pmatrix} 4 & 1 \\ 2 & 3 \end{pmatrix} \]

• A. 3, 4
• B. 5, 2
• C. 4, 1
• D. 6, 1

Hint:

For 2x2 matrices, the eigenvalues can be calculated by solving the characteristic equation $\det(A - \lambda I) = 0$.

Answer 1

The Correct Option is A

To find the eigenvalues, we solve the characteristic equation: \[ \det(A - \lambda I) = 0 \] \[ \det\begin{pmatrix} 4-\lambda & 1 \\ 2 & 3-\lambda \end{pmatrix} = 0 \] \[ (4 - \lambda)(3 - \lambda) - 2 = 0 \] \[ \lambda^2 - 7\lambda + 10 = 0 \] \[ \lambda = 3, 4 \]