# Solving Systems of Linear Equations

A square system of linear equations has the form Ax = b, where A is a user-specified n × n matrix, b is a given n-vector, and x is the solution n-vector. You must specify each entry of A and b. The entire vector x is returned as output.

When A is invertible, a unique solution to Ax = b exists. The most commonly used direct method for solving Ax = b factors the matrix A into a product of triangular matrices and solves the resulting triangular systems of linear equations. Functions that use direct methods for solving systems of linear equations all compute the solution to Ax = b. You can use IDL Analyst functions IMSL_LUSOL, IMSL_CHSOL, and IMSL_CHNNDSOL to compute x.