Learning Objectives:

__Math Tutoring on Using Augmented Matrices__

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An **Augmented Matrix** is a matrix whose elements are the coefficients of a set of simultaneous linear equations with the constant terms of the equations entered in an added column.

An **augmented matrix **is in** ****Row Echelon Form** if the main diagonal consists of **1's or 0's** and all the elements under the main diagonal are **0's. **An **augmented matrix** can be transformed in the following ways to result in an equivalent system of equations known as **Gaussian Elimination**: **1) **Any two **rows** can be **interchanged. **

**2) **The elements of any **row** can be **multiplied** by a **nonzero real** number.

**3)** Any **row** can be **changed** by **adding **or** subtracting** the corresponding elements with another row.

An **augmented matrix** can be written in **row echelon form** and **reduced row echelon form** using the **graphing calculator** also.

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**Hook questions:**

*1. **What is the use of Augmented Matrix?*

*2. **What is Row Echelon Form?*

*3. **What is the goal of transforming Augmented Matrix to Reduced Row Echelon Form?*

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