Question

Eigenvalue question: \[\begin{pmatrix} 6 & 8 \\ 4 & 2 \end{pmatrix} \quad \text{Eigenvalue options:} \quad \text{(i) 1, (ii) 2, (iii) 3, (iv) 4}\]

Hint:

The eigenvalues of a matrix are the solutions to the characteristic equation \( \det(A - \lambda I) = 0 \), where \( \lambda \) represents the eigenvalues.

Answer 1

To find the eigenvalues of the matrix, we need to solve the characteristic equation: \[ \det(A - \lambda I) = 0 \] Where \( A \) is the matrix, and \( I \) is the identity matrix. Solving for the eigenvalues will give us the answer.