Suppose the matrix A is used to transform points in the plane iteratively. That is, given a point v, consider the sequence vn = Anv. Letting U = [u1 u2] so that ui is an eigenvector associated to λi and letting v = c1u1 + c2u2 what is a simple expressions for an and bn so that vn = Anv = anu1 + bnu2. 5/4 -3/4]A :|-3/4 5/4

Given the matrix A=54-34-3454 Diagonalize the matrix A.

Answered: Suppose the matrix A is used to…

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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Suppose the matrix A is used to transform points in the plane iteratively. That is, given a point v, consider the sequence v_n = Aⁿv. Letting U = [u₁ u₂] so that u_i is an eigenvector associated to λ_i and letting v = c₁u₁ + c₂u₂ what is a simple expressions for a_n and b_n so that v_n = Aⁿv = a_nu₁ + b_nu₂.

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Step 1

Given the matrix

$A = [\begin{matrix} \frac{5}{4} & - \frac{3}{4} \\ - \frac{3}{4} & \frac{5}{4} \end{matrix}]$

Diagonalize the matrix A.

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