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Rule of Sarrus Interactive Visualizer

Run the Rule of Sarrus Visualizer Fullscreen

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About This MicroSim

This visualization demonstrates the Rule of Sarrus for computing 3×3 determinants through step-by-step animation.

The method:

  1. Extend the matrix by repeating the first two columns
  2. Add products along the three downward diagonals (green)
  3. Subtract products along the three upward diagonals (red)

Important

The Rule of Sarrus only works for 3×3 matrices. For larger matrices, use cofactor expansion.

How to Use

  1. Step through: Click "Step" to advance one diagonal at a time
  2. Auto-play: Click "Play" to animate automatically
  3. Adjust speed: Use the slider to control animation speed
  4. Try examples: Select Identity, Rotation, or Singular matrix presets

Embedding

1
<iframe src="https://dmccreary.github.io/linear-algebra/sims/sarrus-rule/main.html" height="482px" scrolling="no"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Apply the Rule of Sarrus to compute 3×3 determinants
  2. Identify positive and negative diagonal products
  3. Understand why this method only works for 3×3 matrices

Suggested Activities

  1. Practice computation: Step through each example and verify the calculation
  2. Compare methods: Use Sarrus on a matrix, then verify using cofactor expansion
  3. Predict results: Before stepping through, predict which diagonals will contribute most

Assessment Questions

  1. What is the determinant of the identity matrix? Why does this make sense geometrically?
  2. The example matrix [[1,2,3],[4,5,6],[7,8,9]] has determinant 0. What does this tell you?
  3. How many multiplications does Sarrus require compared to cofactor expansion?

References