Unlocking the Magic of Linear Transformations

• Tertiary Education

Unlocking the Magic of Linear Transformations

Learning Objective

At the end of the lesson you will understand the concept of linear transformations and how to apply them in mathematical contexts.

What do you already know about transforming shapes in math?

What is a Linear Transformation?

A linear transformation is a function between two vector spaces that preserves vector addition and scalar multiplication.

Characteristics of Linear Transformations

Key properties: f(x + y) = f(x) + f(y) and f(cx) = cf(x) for vectors x, y and scalar c.

Matrix Representation

Any linear transformation can be represented using a matrix, allowing easy computation and visualization.

Examples of Linear Transformations

Examples include rotations, reflections, scaling, and shearing, demonstrating diverse applications.

Visualizing Linear Transformations

Interactive element: Use graphing software to explore how transformations alter shapes and vectors.

Applications in Real Life

Used in computer graphics, data analysis, and physics to model and solve real-world problems.

Summary and Q&A

Review key points: definition, properties, matrix representation, and applications. Open floor for questions.

Write down 3 things you learned in this lesson.

Write down 2 things you want to know more about.

Ask 1 question about something you haven't quite understood yet.