Solving Using Row Reduction

Algebra 2 · Axiom Academy

EXAMPLE Solving a System by Row Reduction Complete Gaussian elimination on a 3-variable system, one pivot at a time. Solve the system using row reduction (Gaussian elimination). Nice work! You've completed Gaussian elimination on a 3 ×︎ 3 system. Remember: Pivots are the leading nonzero entries in each row — we scale each one to 1 . Elimination creates zeros below (and, for reduced row echelon form, above) each pivot. Row operations preserve the solution: scaling a row by a nonzero constant, and adding/subtracting a multiple of one row from another. Row echelon form has pivots of 1 with zeros below; reduced row echelon form also has zeros above. The final matrix reads off the solution directly: . This method works for any system of linear equations — one pivot at a time, column by column, left to right.

This is the written version of the interactive lesson above. See the full Algebra 2 course.