The solve() function is useful to solve the system of equation, Ax = b.

In addition to solve(), functions like backsolve() and forwardsolve() are more efficient when A is upper triangular and lower triangular, respectively.

Consider the least squares estimator in linear regression models, , which is the solution to the equation,

Apply the LU factorization on , and use backsolve() and forwardsolve() to recover the least squares estimator displayed below.