Education Technology

Solving with matrices

Activity Overview

Students use Row-Reduction in matrices to solve simultaneous equations. Simultaneous equations with no solutions and infinitely many solutions are explored using matrices and graphs.


  • Introduction to use of matrices to solve systems of linear equations
  • Use of the ‘rref’ function as a useful tool for determining the nature of any solutions


matrix representation, ‘rref’ function, solving systems of equations

About the Lesson

This task is suitable for students in Year 11 mathematics, who have completed some work on solving pairs of simultaneous linear equations. It can be completed in a double lesson. No prior experience of matrices is assumed or is needed. The matrices are used as a relevant representational form for the algorithm. The focus is on the use and interpretation of a matrix solving command rref, short for reduced row echelon form. The rref command employs an iterative algorithm that reduces a system of linear equations to equivalent and unique equations in their simplest form.