Using matrices to solve linear systems

Equivalence of systems of linear equations, row operations, corresponding matrices representing the linear systems

Reduced Row-Echelon Form - A First Course in Linear Algebra

After solving a few systems of equations, you will recognize that it does not matter so much what we call our variables, as opposed to what numbers act as their coefficients. A system in the variables \(x_1,\,x_2,\,x_3\) would behave the same if we changed the names of the variables to \(a,\,b,\,c\) and kept all the constants the same and in the same places. In this section, we will isolate the key bits of information about a system of equations into something called a matrix, and then use this matrix to systematically solve the equations. Along the way we will obtain one of our most important and useful computational tools.

Introductory worksheet on systems of linear equations and augmented matrices Awaiting Moderation

Focus on computations skills. Convert from linear system to augmented matrix and back. Perform row operations. Solutions included. Uncomment \printanswers line before compiling to show solutions.

Solutions of Linear Systems Awaiting Moderation

A short worksheet on solving linear systems.