A discrete system is represented by the difference equation

A discrete system is represented by the difference equation
X₁ (k + 1) a a - 1 X₁(k)
X₂ (k + 1 ) a + 1 a X₂(k)

It has initial conditions X_{1 (0) = 1; X_{2 (0) = 0. The pole locations of the system for a = 1, are}}

From the given difference equation,

A =		a	a - 1
		a + 1	a

The pole locations of the system for a = 1.

Then A =		1	0
		2	1

SI – A| ⇒ (s – 1)² = 0
S = 1 ± j0

	X₁ (k + 1)			a	a - 1			X₁(k)
	X₂ (k + 1 )			a + 1	a			X₂(k)