Augmented Matrices and The Gauss-Jordan Method



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Augmented Matrices and The Gauss-Jordan Method

(Teacher Notes)


Use the information below to set up a system of equations and then solve the system using the elimination method.

An investor has a total of 45 one-ounce ingots, made of either gold or silver, worth $7636.50. The value of a gold ingot is $280.00, and the value of a silver ingot is $4.25. Find g, the number of gold ingots, and s, the number of silver ingots?

(Released TAKS – July 2006)

System of Equations Augmented Matrices




Answer:


1st : Find s by eliminating g.



2nd : Find g by eliminating s in R1.

The process used above is called The Gauss-Jordan Elimination Method. This is a systematic way to solve system of equations and is especially helpful when solving very large systems of equations. The first step in using the Gauss-Jordan Elimination Method is to use the system of equations to set up an augmented matrix (a coefficient matrix next to a constant matrix) . For the problems below, set up a system of equations and the corresponding augmented matrix.


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