I have a tridiagonal matrix that I am trying to simplify into an upper triangular matrix using Mathematica, so I can use back substitution and solve my linear system. I have found the command "RowReduce" but that simplifies the matrix to far and I get an identity matrix since the matrix I am trying to simplify is a square matrix. Is there a way in Mathematica to simplify a matrix into an upper triangular matrix?
Note: I want to solve the linear system by hand. I just want Mathematica to simplify the matrix.
Update: Specifically, I'd like to get an upper triangular matrix by using Gaussian elimination.