Let & denote the vector space of all functions &: R&R under the usual operations of function addition and scalar multiplication of functions. Let It be the subspace of I sponned by the two functions sint and cost, and let B = { sint, costs, which is a basis for H. a) Let T: HH be defined by T(F) = f'. ie, I takes the first derivative. Find the matrix [T]B for the linear transformation T relative to the basis B. b) Let f(t) = 4 cos (t-3). Use the trigonometric identity COS (CA-B) = cos A cos B + Sin A sin B to show that f is in the subspace H. Then give the coordinate Vector []B. C) Let K= Span (sint, cost, 4 cos (t-24)}, which is a subspace of F. Give dim k.
Let & denote the vector space of all functions &: R&R under the usual operations of function addition and scalar multiplication of functions. Let It be the subspace of I sponned by the two functions sint and cost, and let B = { sint, costs, which is a basis for H. a) Let T: HH be defined by T(F) = f'. ie, I takes the first derivative. Find the matrix [T]B for the linear transformation T relative to the basis B. b) Let f(t) = 4 cos (t-3). Use the trigonometric identity COS (CA-B) = cos A cos B + Sin A sin B to show that f is in the subspace H. Then give the coordinate Vector []B. C) Let K= Span (sint, cost, 4 cos (t-24)}, which is a subspace of F. Give dim k.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...
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