General usage:
* The decision was made by the highest echelon of the company.
* The leak of information came from a high echelon within the government.
* The news spread through the echelons of the military.
Figurative usage:
* She climbed the echelons of success, achieving her goals one step at a time.
* His work was lauded by the highest echelons of the scientific community.
* The young artist quickly rose through the echelons of the art world.
In the context of mathematics:
* We used Gaussian elimination to reduce the matrix to echelon form.
* The system of equations was solved by applying row operations until it reached echelon form.
The best way to use "echelon" depends on the context of your sentence.