Question

The highest Eigen value of the 2 × 2 matrix \(\begin{bmatrix} 1 & 2 \\\ 4 & 3 \end{bmatrix}\) is
1. -1
2. -5
3. 5
4. 1

Answer 1

Correct Answer - Option 3 : 5

Characteristic equation,

|A - λI| = \(\left| \begin{matrix}1 - λ & 2 \\\ 4 & 3 - λ \end{matrix}\right|=0\)

⇒ λ² - 4λ - 5 = 0

⇒ λ = 5, -1

∴ λ_max = 5