Precalculus: Linear Transformations

Objectives

• Students will use matrices to help visualize and describe linear transformations.
• Students will manipulate the input vector and observe the results of specific linear transformations geometrically.
• Students will generate output vectors.
• Students will characterize linear transformations in terms of vector magnitude and angles.

Vocabulary

• linear transformation
• transformation matrix
• reflection
• rotation
• scaling
• projection

About the Lesson

This lesson involves linear transformations from R² to R² represented by matrices. Note: R² = R x R represents the set of all pairs of real numbers.
As a result, students will:

• Grab and drag the input vector and observe the effect of each linear transformation.
• Describe each linear transformation in words.
• Compute output vectors in order to confirm conjectures.
• Determine general properties of certain linear transformations.