Suppose the 9-vector x = : (1, 1, 2, 3, 2, 1, 0, —1, 0) represents a time series.(a) We wish to calculate a new vector y equal to the cumulative sum of the elements of x, i.e.,Find So. What are its dimensions?y =X1x1 + x₂x1 + x₂ + x3 = S9x.Σ₁11x₁(b) Calculate y = S9x.(c) We wish to calculate a new vector z equal to the difference between neighboring elements in y, i.e.,Z =Y2 - Y₁Y3 - Y2:Ly9 - Y8= Dgy.=Find Do. What are its dimensions?(d) Calculate z = : Doy. What do you notice about z with respect to x?(e) Suppose you wish to find a matrix A such that z' = Ay = x. Find A.Hint: Make a simple modification to D9.(f) Compute AS9. Does this result surprise you? Why or why not?(g) Graphically compare x, y, and z. How are they related?

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Answered: Suppose the 9-vector x = (1, 1, 2, 3,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose the 9-vector x = (1, 1, 2, 3, 2, 1, 0, -1, 0) represents a time series. (a) We wish to calculate a new vector y equal to the cumulative sum of the elements of x, i.e., Find So. What are its dimensions? (b) Calculate y = S9x. X1 x1 + x₂ y = x₁ + x₂ + x3 = S9x. Σ₁=1 Xi