Solving 2×2 and 3×3 Systems with Cramer’s Rule

This GeoGebra example demonstrates a step-by-step workflow for solving linear equation systems of sizes 2×2 and 3×3 using Cramer’s Rule. It highlights how determinants of a coefficient matrix and determinant values of column-replaced matrices lead directly to the solution components. Key concepts include linear systems, matrices, determinants (determinant-based computation), and the Cramer’s Rule mechanism: replace one column with the constants vector to form numerators, divide by the determinant of the original coefficient matrix (the denominator). Construction-wise, the model uses Determinant to compute all needed determinants, Textfield to input coefficients/constant terms, SelectedIndex to choose whether the case is 2×2 or 3×3, and If to switch logic between branches. It defines matrix entries a11–a33 and constants b1–b3, builds main matrices A2/A3 and corresponding replacement matrices (B2/B3, A2X/A2Y, A3X/A3Y/A3Z), computes denominator determinants dA2/dA3 and numerator determinants dA2X/dA2Y and dA3X/dA3Y/dA3Z, and outputs solution variables case2SolX/case2SolY and case3SolX/case3SolY/case3SolZ. Suitable for high school advanced algebra, early undergraduate linear algebra, and math instruction where understanding determinant-based solving is the goal.