Let M be a 2 × 2 matrix with eigenvalues ₁ = -1.2, A2 = 1 with corresponding eigenvectorsConsider the difference equationwith initial condition Xo=53V₁ =V2 =2xk+1 =MxkWrite the initial condition as a linear combination of the eigenvectors of M.That is, write x0 = c1V1 + C₂ V₂ =In general, xk=V1+V2) * vi+k) v2Specifically, x4 =For large k, xk≈k

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2X2 matrix with eigenvalues A₁ =-1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo= [3]. V₁ = V2 Xk+1 = MX Write the initial condition as a linear combination of the eigenvectors of M. That is, write Xo = c1V1 + C2V2= In general, Xk= V₁+ V2 )* VI+ Specifically, X4=

2X2 matrix with eigenvalues A₁ =-1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo= [3]. V₁ = V2 Xk+1 = MX Write the initial condition as a linear combination of the eigenvectors of M. That is, write Xo = c1V1 + C2V2= In general, Xk= V₁+ V2 )* VI+ Specifically, X4=

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 26EQ

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