7.6-02 Fibonacci as a matrix recurrence

Fibonacci as a matrix recurrence

Model the Fibonacci recurrence as a two-component matrix update and recover its closed form from eigenmodes. The progression emphasizes state ordering, initial data and the distinction between a general recurrence and one specific sequence.

What you will practise

• Construct the recurrence matrix
• Find its characteristic roots
• Match initial data to mode coefficients
• Interpret the dominant growth contribution

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review recurrences, diagonalization and quadratic roots. The questions move from recognition and short calculations to connected reasoning. Single-select questions require one answer; multiselect questions ask you to evaluate every statement independently.

A final change of initial data shows how the same update matrix can produce a different closed-form sequence. Work out your own result before checking the choices, then use the explanation to compare the reasoning and diagnose a mistaken assumption. This focused practice connects conceptual understanding with reliable problem solving and supports review before the next microlearning.