Task 3: (a) Define the concept of linear dependence. Consider the functions cos²x, sin²x and cos(2x) as vectors in F(R) (the vector space of all functions on R) (b) Show that these are linearly dependent (lead: addition formula), and that: If you remove any one of the 3 polynomials, the two remaining polynomials become linearly independent.

Task 3: (a) Define the concept of linear dependence. Consider the functions cos²x, sin²x and cos(2x) as vectors in F(R) (the vector space of all functions on R) (b) Show that these are linearly dependent (lead: addition formula), and that: If you remove any one of the 3 polynomials, the two remaining polynomials become linearly independent.

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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