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
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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
Related questions
Question
![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 =
X1
x1 + x₂
x1 + 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 - Y₁
Y3 - 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1da88d38-e18c-40f1-9bb8-69bad3269ec7%2F070580f9-6660-4320-a0a9-1a6501d53472%2Fymzi5wj_processed.png&w=3840&q=75)
Transcribed Image Text: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 =
X1
x1 + x₂
x1 + 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 - Y₁
Y3 - 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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