7.B-02 Recurrences and initial states

Recurrences and initial states

Translate scalar recurrences into evolving states with clearly specified initial data. The exercises connect repeated updates, state-vector ordering and closed-form checks without assuming prior dynamical-systems experience.

What you will practise

• Iterate a recurrence reliably
• Identify required initial data
• Construct a two-component state
• Distinguish linear and affine updates

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review basic algebra and matrix–vector multiplication. 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.

The final closed-form check requires both the update rule and the initial value to agree. 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.