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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• Introduction to Matrices
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We use the identity matrix to calculate a the inverse of a square matrix. In order to be invertible, a matrix must be square. By finding the square matrix inverse, we can find the solution of a system of linear equations. A square matrix inverse, when multiplied on the left or right by the original matrix gives us the identity matrix.

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• Systems of Linear Equations and Matrices
• How Do You Solve Linear Systems Using Matrix Algebra?
• The Identity Matrix

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Equations are fundamental to Algebra, and solving linear equations is necessary for you to learn how to solve two-step equations, and other multi-step equations. Solving linear equations involves finding the value for the variable that makes the statement true using additive and multiplicative inverses.

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Brightstorm Lessons

• How Do You Solve For a Parameter in a Linear Equation?
• How Do You Apply Linear Equations to Geometry Problems?
• How Do You APply Linear Equations to Distance Problems?

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