2. Consider the Fibonacci-like numbers given by Go = 0, G1 =1 and Gr+2 = 2G,+Gr+1• (a) Write down the first 10 numbers in the sequence. %3D %3D [Gr+1 G, A (b) Write down a matrix equation for the numbers of the form [Gr+2] Gr+1 (c) Find the eigenvalues of the resulting matrix A. (d) Hence find a formula for Gr+2 in terms of r, following the method in the lectures using the diagonalization of A.

2. Consider the Fibonacci-like numbers given by Go = 0, G1 =1 and Gr+2 = 2G,+Gr+1• (a) Write down the first 10 numbers in the sequence. %3D %3D [Gr+1 G, A (b) Write down a matrix equation for the numbers of the form [Gr+2] Gr+1 (c) Find the eigenvalues of the resulting matrix A. (d) Hence find a formula for Gr+2 in terms of r, following the method in the lectures using the diagonalization of A.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8BEXP

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