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2×2 Determinant Calculator

Run the 2×2 Determinant Calculator Fullscreen

Edit the MicroSim with the p5.js editor

About This MicroSim

This interactive calculator helps you practice computing 2×2 determinants while seeing the geometric interpretation as the signed area of a parallelogram.

Features:

  • Editable matrix: Click cells to enter custom values
  • Step-by-step calculation: See ad - bc computed explicitly
  • Geometric visualization: Watch the parallelogram formed by column vectors
  • Color coding: Green (positive), red (negative), gray (zero/singular)

How to Use

  1. Click matrix cells to edit values (use keyboard to type, Enter to confirm)
  2. Use preset buttons for quick examples:
  3. Random: Generate a random matrix
  4. Identity: The identity matrix (det = 1)
  5. Singular: A matrix with determinant 0
  6. Toggle "Show Steps" to see the calculation breakdown

Embedding

1
<iframe src="https://dmccreary.github.io/linear-algebra/sims/det-2x2-calculator/main.html" height="482px" scrolling="no"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Calculate 2×2 determinants using the formula det(A) = ad - bc
  2. Identify the main diagonal and anti-diagonal of a matrix
  3. Connect algebraic computation to geometric area

Suggested Activities

  1. Practice computation: Enter 5 different matrices and verify your mental calculations
  2. Find singular matrices: Try to create matrices with determinant exactly 0
  3. Explore patterns: What happens when you scale a row by k?

Assessment Questions

  1. What is the determinant of [[2, 3], [4, 6]]? Why is this predictable from the matrix structure?
  2. If det(A) = 5, what is det(2A)?
  3. Create a matrix with determinant exactly -12.

References