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Let f(x) = sin x and g(x) = cos x, and W = span{f, g}. 10.1 Use the Wronskian to show that f and g are linearly independent.

Let f(x) = sin x and g(x) = cos x, and W = span{f, g}. 10.1 Use the Wronskian to show that f and g are linearly independent.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Let f(x) = sin x and g(x) = cos x, and W = span{f, g}.
10.1 Use the Wronskian to show that f and g are linearly independent. 
10.2 For a ∈ R, let f1(x) = sin(x + a) and g1(x) = cos(x + a). Show that f1, g1 ∈ W. 
10.3 Show that {f1, g1} is linearly independent

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