Sistema Linear 3×3 (Cramer)

The 3×3 Linear System Calculator solves systems of three equations with three unknowns (x, y, z) using Cramer's Rule. The method calculates the determinant of the main matrix (det) and the determinants of the modified matrices (det_x, det_y, det_z), where each column is replaced by the constants. The solutions are given by x = det_x/det, y = det_y/det, z = det_z/det, provided det ≠ 0.

This tool is useful for students of linear algebra, engineering, and exact sciences who need to solve linear systems quickly. For example, in problems involving electrical circuits, chemical equilibrium, or analytic geometry, 3×3 systems frequently appear. The calculator automates the calculations, avoiding manual errors and saving time.

Important precautions: Cramer's Rule only works if the main determinant is non-zero (consistent and independent system). If det = 0, the system may be inconsistent or have infinite solutions. Additionally, for large systems, other methods (like Gaussian elimination) are more efficient. Ensure coefficients are entered correctly, including negative signs.

The calculator accepts integer or decimal numbers. Results are displayed with up to 4 decimal places. For systems with zero determinant, an error message will be shown. Use a period as decimal separator and avoid fractions, converting them to decimals before entering.