To solve a system of linear equations, we can use substitution, elimination or something we call augmented matrices. To use matrices to solve a system of linear equations, we first enter the values associated with each of the variables and the answer. Once we put the information into a matrix (a rectangular array of numbers), we can use matrix operations to solve the equation.

Example of an Augmented Matrix

augmented matrix

Definitions:

• Elements: Each of the entries in the augmented matrix
• Rows: The numbers or variables that run across the matrix.
• Columns: The numbers or variables that run down the matrix.
• The diagonal of the matrix: The set of elements that starts at the top, left corner and runs diagonally down and to the right. (This diagonal: 2, -1 and 4.)

What Is An Augmented Matrix?

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Systems of equations are concepts that first show up in Algebra I. Systems of equations are problems with two or more equations that contain the same variables. There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

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