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 & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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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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