Final answer:
To find x₁, x₂, and x₃ using the difference equation, we can apply the equation x(n+1) = A * x(n) repeatedly. By substituting the given values for A and x₀ into the equation, we can calculate the values for x₁, x₂, and x₃ step by step.
Step-by-step explanation:
In this question, we are given A = [2 -1 -1 2] and x₀ = [3 1]. We are asked to find x₁, x₂, and x₃ using the difference equation. To do this, we need to apply the difference equation repeatedly. The difference equation is given by:
x(n+1) = A * x(n)
Let's calculate x₁, x₂, and x₃ step by step:
x₁ = A * x₀ = [2 -1 -1 2] * [3 1] = [2*3 + (-1)*1, (-1)*3 + 2*1] = [5, -1]
x₂ = A * x₁ = [2 -1 -1 2] * [5, -1] = [2*5 + (-1)*(-1), (-1)*5 + 2*(-1)] = [11, -7]
x₃ = A * x₂ = [2 -1 -1 2] * [11, -7] = [2*11 + (-1)*(-7), (-1)*11 + 2*(-7)] = [29, -1]