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Let W = span(1, x, x², sin(x), cos(x), e) and T : W → W be defined by d d² T(f) = - dx2 f(x) – 2 f(x). dx and let B = (1, x, x², sin(x), cos(x), e²). (a) Find a matrix A = R6×6 so that for all fЄ W. (b) Find a basis for ran(A) and ker(A) (c) Find one solution to [T(ƒ)] = A[f] × 2 0 0 Ax = −1 2 0

Let W = span(1, x, x², sin(x), cos(x), e) and T : W → W be defined by d d² T(f) = - dx2 f(x) – 2 f(x). dx and let B = (1, x, x², sin(x), cos(x), e²). (a) Find a matrix A = R6×6 so that for all fЄ W. (b) Find a basis for ran(A) and ker(A) (c) Find one solution to [T(ƒ)] = A[f] × 2 0 0 Ax = −1 2 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with solution with steps for parts a,b,c,d

(d) Notice that T(ƒ) = 2 − sin(x) + 2 cos(x) exactly when A[ƒ]× = (2,0,0, −1, 2,0). Find all solutions in W to that is, find the set d² dx2f(x) – 2- d dx -ƒ(x) = 2 − sin(x) + 2 cos(x), {ƒ ≥ W : T(ƒ) = 2 - sin(x) + 2 cos(x)}.
Transcribed Image Text:(d) Notice that T(ƒ) = 2 − sin(x) + 2 cos(x) exactly when A[ƒ]× = (2,0,0, −1, 2,0). Find all solutions in W to that is, find the set d² dx2f(x) – 2- d dx -ƒ(x) = 2 − sin(x) + 2 cos(x), {ƒ ≥ W : T(ƒ) = 2 - sin(x) + 2 cos(x)}.
Let W = span(1, x, x², sin(x), cos(x), e) and T : W → W be defined by d d² T(f) = - dx2 f(x) – 2 f(x). dx and let = (1, x, x², sin(x), cos(x), e²). (a) Find a matrix A = R6×6 so that for all fЄ W. (b) Find a basis for ran(A) and ker(A) (c) Find one solution to [T(ƒ)] = A[f] × 2 0 0 Ax = −1 2 0
Transcribed Image Text:Let W = span(1, x, x², sin(x), cos(x), e) and T : W → W be defined by d d² T(f) = - dx2 f(x) – 2 f(x). dx and let = (1, x, x², sin(x), cos(x), e²). (a) Find a matrix A = R6×6 so that for all fЄ W. (b) Find a basis for ran(A) and ker(A) (c) Find one solution to [T(ƒ)] = A[f] × 2 0 0 Ax = −1 2 0
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