In the space C[0, π] let f, g, h, and j be the vectors defined by f(x) = 1 g(x) = x h(x) = COS X j(x) = cos2 2 or 0≤x≤ T. Show that f, g, h, and j are linearly dependent by writing j as a linear combination of f, g, and h. Answer: i = f+ 9 + h.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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In the space C[0, π] let f, g, h, and j be the vectors defined by
f(x) = 1
g(x) = X
h(x) = cos x
j(x) = cos²
x
2
for 0≤x≤T. Show that f, g, h, and j are linearly dependent by writing j as a linear
combination of f, g, and h.
Answer: j =
_f+g+
h.
Transcribed Image Text:In the space C[0, π] let f, g, h, and j be the vectors defined by f(x) = 1 g(x) = X h(x) = cos x j(x) = cos² x 2 for 0≤x≤T. Show that f, g, h, and j are linearly dependent by writing j as a linear combination of f, g, and h. Answer: j = _f+g+ h.
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