Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

In Exercise 7, do the parts of Exercise 1 for the given linear transformation, bases, and vector v.

Please solve question #7, ONLY question #7. PLEASE write it on PAPER. 

1. Let T: R² → R2 be the linear transformation + x₂ [3]-[***] T X2 a) Find [7] where a is the standard basis for R². b) Let 6 be the basis consisting of 1 [3][7] -1 for R2. Find the change of basis matrix from a to B. c) Find the change of basis matrix from ß to a. d) Find [7]. e) Find [v]s for V= <-2 f) Find [T(v)]. g) Use the result of part (f) to find T (v).
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Transcribed Image Text:1. Let T: R² → R2 be the linear transformation + x₂ [3]-[***] T X2 a) Find [7] where a is the standard basis for R². b) Let 6 be the basis consisting of 1 [3][7] -1 for R2. Find the change of basis matrix from a to B. c) Find the change of basis matrix from ß to a. d) Find [7]. e) Find [v]s for V= <-2 f) Find [T(v)]. g) Use the result of part (f) to find T (v).
7. D: V→ V where V is the set of solutions to the differential equation y" + y = 0; a the basis of V consisting of sin x, cos x; ß the basis consisting of sin x + cos x, sin x - cos x; v = 3 cos x - 2 sin x.
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Transcribed Image Text:7. D: V→ V where V is the set of solutions to the differential equation y" + y = 0; a the basis of V consisting of sin x, cos x; ß the basis consisting of sin x + cos x, sin x - cos x; v = 3 cos x - 2 sin x.
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