Education Technology

Precalculus: Linear Transformations

by Texas Instruments


  • 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.


  • 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.