7.6-12 Trace–determinant portraits

Trace–determinant portraits

Locate real planar continuous systems in the trace–determinant classification. Use the discriminant to distinguish nodes and spirals, and inspect boundary cases where trace and determinant alone leave important structure unresolved.

What you will practise

• Classify by trace and determinant
• Interpret the discriminant
• Identify centers and saddles
• Analyze a parameter family

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review quadratic characteristic equations and continuous-time stability. 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 parameter example combines a fixed rotation rate with a variable real growth rate. 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.