Augmented Matrices and The Gauss-Jordan Method
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Problem #3: A theater has a seating capacity of 900 and charges $2 for children, $3 for students, and $4 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $2800. How many children attended the show? Answer: Let a = number of adults that attended the show s = number of students that attended the show c = number of children that attended the show  
The goal in Gauss-Jordan Elimination is to use row operations (interchange two rows, multiply a row by a nonzero constant, add two rows, or add a multiple of one row to another row) to change the augmented matrix to row reduced echelon form (rref) which looks like the following matrix: 
Notice the right hand side is the identity matrix while the left hand side can be any numbers. Why do you think we want to convert the augmented matrix to the ‘identity-like” matrix above? To get a matrix in row reduce echelon form follow the method suggested below. Use row operations to make  . Then use row operations to make the other elements in column 1 zero.
First: 
Use row operations to make  . Then use row operations to make the other elements in column 2 zero.
Second:
Use row operations to make  . Then use row operations to make the other elements in column 3 zero.
Third:
Use the augmented matrices set up above and perform row operations to get each of the augmented matrices in row reduced form. Download 0.67 Mb. Share with your friends:
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