Let M be a 2 x 2 matrix with eigenvalues 11 = 0.9, 12 = -0.25 with corresponding eigenvectors V1 = , V2 = Consider the difference equation Xk+1 Mxx [5 with initial condition x, = Write the initial condition as a linear combination of the eigenvectors of M. That is, write xo = c¡V1 + C2V2 = -2.5 V1+ -5 V2 In general, Xg = (0.9 Vị+ -5 (-0.25 -2.5 4.05 Specifically, x2 = -3.425

Let M be a 2 x 2 matrix with eigenvalues 11 = 0.9, 12 = -0.25 with corresponding eigenvectors V1 = , V2 = Consider the difference equation Xk+1 Mxx [5 with initial condition x, = Write the initial condition as a linear combination of the eigenvectors of M. That is, write xo = c¡V1 + C2V2 = -2.5 V1+ -5 V2 In general, Xg = (0.9 Vị+ -5 (-0.25 -2.5 4.05 Specifically, x2 = -3.425

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...

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