Show by induction that solutions to initial value problems are unique. In other words, show that if a0,a1,... and b0,b1,... are two sequences which are both solutions to the same recurrence relation of order k, then an = bn for all n ≥ 0 if ai = bi for all 0 ≤ i < k.

Show by induction that solutions to initial value problems are unique. In other words, show that if a0,a1,... and b0,b1,... are two sequences which are both solutions to the same recurrence relation of order k, then an = bn for all n ≥ 0 if ai = bi for all 0 ≤ i < k.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 56EQ

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Question

Show by induction that solutions to initial value problems are unique. In other words, show that if a₀,a₁,... and b₀,b₁,... are two sequences which are both solutions to the same recurrence relation of order k, then a_n= b_nfor all n ≥ 0 if a_i= b_ifor all 0 ≤ i < k.