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Let f(x) = sin x and g(x) = cos x, and W = span{f,g}. Use the Wronskian to show that f and g are linearly independent. For a R, let fi(x) = sin(x + a) and g₁(x) = cos(x + a). Show that f1,91 € W. Show that {f1,91} is linearly independent.

Let f(x) = sin x and g(x) = cos x, and W = span{f,g}. Use the Wronskian to show that f and g are linearly independent. For a R, let fi(x) = sin(x + a) and g₁(x) = cos(x + a). Show that f1,91 € W. Show that {f1,91} is linearly independent.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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Let f(x) = sinx and g(x)= = cos x, and W = span{f,g}. Use the Wronskian to show that f and g are linearly independent. For a ER, let fi(x) = sin(x + a) and g₁(x) = cos(x + a). Show that f₁,91 € W. Show that {f1, 91} is linearly independent.
Transcribed Image Text:Let f(x) = sinx and g(x)= = cos x, and W = span{f,g}. Use the Wronskian to show that f and g are linearly independent. For a ER, let fi(x) = sin(x + a) and g₁(x) = cos(x + a). Show that f₁,91 € W. Show that {f1, 91} is linearly independent.
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