Math Visualization List
Calculus
First Derivative Second Derivative Integration
Determinant
2x2 & 3x3 Determinants Cramer's Rule Permutations & Inversions Permutation Definition & Expansion Properties of Determinants: Row Operations Minors & Cofactors Two-Row Laplace Expansion Vandermonde Determinant
Matrix Operations
Matrix Addition, Subtraction & Scalar Multiplication Matrix Multiplication & Power Transpose, Determinant & Adjoint Inverse Matrix & Matrix Equations Elementary Transformations, Echelon & Canonical Form
Probability & Statistics
Conditional Probability, Independence & Total Probability Discrete Probability Distributions PMF & CDF 2D Random Vectors Conditional Probability Distributions Bayes' Theorem Numerical Characteristics of Random Variables Higher Moments & Covariance Matrix Law of Iterated Expectations Independence, Mean Independence & Uncorrelated Continuous Statistical Distributions
Vector Operations
Vector Addition, Subtraction & Scalar Multiplication Linear Combination, Span & Basis Matrices as Transformations Composition of Transformations 3D Linear Transformations Determinant Inverse, Column Space & Rank Cross-Dimensional Transformations Vector Angle Cross Product Change of Basis Eigenvectors & Eigenvalues Function Vector Spaces Geometric Interpretation of Cramer's Rule Gravity Simulation

Properties of Determinants: Row Operations Experiment

Elementary Row Operations

1) Swap Two Rows R ↔ R
2) Multiply Row by Constant R ← × R
3) Add Multiple of Row to Another R ← R + ×R

Verification Log

Basic Introduction

Three Core Properties

  • Swapping two rows: det changes sign.
  • Multiplying a row by constant k: det is multiplied by k.
  • Adding a multiple of one row to another: det remains unchanged.

This page demonstrates these three properties through "predicted vs actual" comparison. After each operation, the system recalculates the determinant and automatically verifies it.

You can perform multiple consecutive operations to observe how properties combine.