Let V be the space spanned byf1 = sin x and f 2 = cos x. (a) Show that gi = 2sin x + cos x and g2 = 3cos x form a basis for V. (b) Find the transition matrix from B' = {g1, g2} to B= {f1,f2}. (c) Find the transition matrix from B to B'. (d) Compute the coordinate vector [h] g, where h=2sin x - B 5cos x, and obtain [h]g'. (e) Check your work by computing [h]g' directly.
Let V be the space spanned byf1 = sin x and f 2 = cos x. (a) Show that gi = 2sin x + cos x and g2 = 3cos x form a basis for V. (b) Find the transition matrix from B' = {g1, g2} to B= {f1,f2}. (c) Find the transition matrix from B to B'. (d) Compute the coordinate vector [h] g, where h=2sin x - B 5cos x, and obtain [h]g'. (e) Check your work by computing [h]g' directly.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 18CM
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