Correct Option: A

Given : A =		2			2
		1			3

Characteristic equation is | A – λI| = 0

⇒		2-λ			2		= 0
		1			3-λ

⇒ (2 – λ) (3 – λ) – 2 = 0
⇒ λ² – 5 + 4 = 0
⇒ λ = 1, 4
Eigen vector for λ = 1 is

		2-λ			2			x1		= 0
		1			3-λ			x2

⇒		1			2			x1		= 0
		1			1			x2

⇒ x₁ + 2x₂ = 0
⇒ x₂ = - 1/2 x
i.e. x₁ : x₂ = – 2 : 1

Since choice (a)		2		is in same ratio of x1 to x2
		-1

∴ choice (a) is an eigen vector.