While reading the book Numerical Methods for Engineers by Steven Chapra and Raymond Canale, I came across a problem in Gauss-Jordan elimination. The problem says,
$$2x_1+x_2-x_3=1\\ 5x_1+2x_2-2x_3=-4\\ 3x_1+x_2+x_3=5$$
to solve this using Gauss-Jordan but without employing pivoting. So far I only know that in order to solve this I need to use pivot to make the 3 rows to contain only one 1.
What are the algorithm to solve this without pivoting?