Outline

• Understanding Gaussian-Elimination and Row-Echelon Form

• Understanding Gauss-Jordan Elimination and Reduced Row-Echelon Form

• Examples to determine whether or not a matrix is in Row-Echelon Form or in Reduced Row-Echelon Form

• Understanding Elementary Row Operations to Rewrite Systems of Linear Equations in Row-Echelon Form and Reduced Row-Echelon Form

• Using Gaussian Elimination and Gauss-Jordan Elimination to Solve Systems of Linear Equations

Note:

Elementary Row Operations are explained later in this discussion.

Determine whether or not the following matrices are in Row-Echelon Form or Reduced Row-Echelon Form

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

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How to Use Gaussian Elimination and Gauss-Jordan Elimination to Solve Linear Systems of Equations

First, let us understand Elementary Row Operations

Use Gaussian Elimination with Back-Substitution or Gauss-Jordan Elimination to solve the linear system of equations.

Example 1

Example 2

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