AI-HL 1.15.1 Eigenvalues and eigenvectors

 Overview

This comprehensive Maths lesson introduces one of the most powerful concepts in linear algebra — Eigenvalues and Eigenvectors — in a way that’s both visual and accessible for IB students. The presentation guides learners step-by-step through the process of finding eigenvalues by solving the characteristic equation det⁡(A−λI)=0 and determining the corresponding eigenvectors through (A−λI)x = 0 .

Teachers will find clear explanations, worked examples, and visual connections that help students understand not only how to compute eigenvalues and eigenvectors, but also why they matter in transformations and matrix applications.

 What’s Inside

• Intuitive explanation of what eigenvalues and eigenvectors represent
• Clear derivation of the characteristic equation
• Step-by-step examples with both real and complex eigenvalues
• Guided methods for solving using the GDC and manual algebraic steps
• Fully worked examples with annotations and visual aids
• Perfectly aligned with IB Mathematics AI HL Topic 1.15.1

 Learning Outcomes

By the end of this lesson, students will be able to:

• Define and explain eigenvalues and eigenvectors conceptually and algebraically
• Solve for eigenvalues using determinants
• Find corresponding eigenvectors through systems of linear equations
• Apply their understanding to real-world transformations and advanced matrix operations

 Why Teachers Love It

This ready-to-use resource makes teaching eigenvalues and eigenvectors straightforward and engaging. It includes visual slides, worked examples, and guided explanations that encourage deep conceptual understanding — saving teachers valuable planning time.

Content:

• PowerPoint presentation

File size:

• PPTX (390 KB)

Number of slides:

16 slides