Question

If A = [2 -1 -1 2] and x₀ = [3 1], find x₁, x₂, and x₃ using the difference equation is ___?

Answer 1

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]