Consider the following linear non-homogeneous recurrence relation where g0=1,g1=3 and gn+1=7gn−10gn−1+2n−3 for n≥1. The reduced closed form of gn can be represented as gn=1/A (P×pn+Q×qn+Rn+S) where p and q are the solutions of the characteristic equation of the recurrence. Given that, p is smaller than q. Here, P,Q,R,S,A are all integers. 1. What is the value of P? 2. What is the value of Q? 3. What is the value of R+S? 4. What is the value of A?

Consider the following linear non-homogeneous recurrence relation where g0=1,g1=3 and gn+1=7gn−10gn−1+2n−3 for n≥1. The reduced closed form of gn can be represented as gn=1/A (P×pn+Q×qn+Rn+S) where p and q are the solutions of the characteristic equation of the recurrence. Given that, p is smaller than q. Here, P,Q,R,S,A are all integers. 1. What is the value of P? 2. What is the value of Q? 3. What is the value of R+S? 4. What is the value of A?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 42EQ

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