Using Augmented Matrices

Tutoring on Using Augmented Matrices

Learning Objectives:

Understand to solve System Of Equations Using an Augmented Matrix (Row Echelon Form).

Math Tutoring on Using Augmented Matrices

 

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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