A powerful and intuitive tool for solving systems of linear equations using Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination, and LU Decomposition.
Cramer’s Rule
a method for solving systems of linear equations using determinants.
It finds each variable by replacing columns of the coefficient matrix
with constants, and works only when the determinant of the matrix is not zero.
It's best for small systems with unique solutions.
a method that simplifies a matrix to solve linear systems by eliminating variables
step-by-step.
Gauss-Jordan extends this by reducing the matrix further to get the exact solution
directly.
This approach works for any system of linear equations.
is a method that breaks a matrix into a lower and an upper triangular matrix.
This helps solve linear equations efficiently by simplifying the system into easier
parts.
It works for square matrices and speeds up repeated calculations.