Let F be the vector space of infinitely differentiable functions from R to R. Consider the subspace: W = span{e^t, sin(2t), cos(3t)} 1. Show that the three vectors above are linearly independent. Consider the linear operator T: W–>W T(f) = f"(t) – af(t) = ( - al) (f). || | dt2 For which real values of a is T invertible 2.

Let F be the vector space of infinitely differentiable functions from R to R. Consider the subspace: W = span{e^t, sin(2t), cos(3t)} 1. Show that the three vectors above are linearly independent. Consider the linear operator T: W–>W T(f) = f"(t) – af(t) = ( - al) (f). || | dt2 For which real values of a is T invertible 2.

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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Question

Let F be the vector space of infinitely differentiable functions from
R to R. Consider the subspace:
W = span{e^t, sin(2t), cos(3t)}
1. Show that the three vectors above are linearly
independent.
Consider the linear operator T: W–>W
T(f) = f"(t) – af(t) = ( - al) (f).
||
|
dt2
For which real values of a is T invertible
2.

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