Consider the differential equation 8y"+y'-6y = 0 and its corresponding linear transformationT(y) = 8y"+y'—6y . Let B = { −8 − 3x + x², −13 − 5x + 2x²,8 + 3x} be a basis for P₂ . Find thematrix for T with respect to B.

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Answered: Consider the differential equation…

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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( 3). Consider the system of equations x' = Ax where A = The eigenvalues for the matrix A are d1 = 2, A2 = 3. Find the corresponding eigenvectors vị and v2.
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V =R * R 10a6b T(") - (170-100) {(2)· (3)} B = { find the matrix representation of T with respect to beta. Then determine wether beta is a basis consisting of eigenvectors. I have got -2 [T]₁ = ( 2 4 this does not match answer key. What's wrong? please point it out and have the rest of solution to the problem. thanks!
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Consider the differential equation 8y"+y'-6y = 0 and its corresponding linear transformation = T(y) = 8y"+y'-6y . Let B {−8 − 3x + x², −13 − 5x + 2x²,8 + 3x} be a basis for P₂ . Find the matrix for Twith respect to B.