Solving the Given Augmented Matrices by ClassOf1

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Sub: Mathematics                                                                     Topic: Linear Algebra

Solving the Given Augmented Matrices

Question:
A group of students decides to sell pizzas to help raise money for their senior class trip. They sold
pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total
of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up
a system of three equations and three unknowns, use an augmented matrix to solve.

 12 10      8 5900
 1     1    1    600
 0      1 1      175


Solve for the matrix.

Solution:

                                            5     2 1475
                                      1
                                            6     3   3                   1
The augmented matrix gives 1                1     1 600          R1         R1
                                                                         12
                                      0      1 1       175


                           5      2 1475
                       1
                           6      3   3
                           1      1 325
To make a21      0, 0                            R2        R1    R2
                           6      3   3
                       0    1     1 175



                       1   0       1 50
                           1      1 325
To make a12      0, 0                            R1       5R2      R1
                           6      3  3
                       0    1     1 175

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 *The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
                                submitting the same in lieu of their academic submissions for grades.
Sub: Mathematics                                                                     Topic: Linear Algebra

                      1    0         1     50
To make a22 1 , 0          1       2     650        R2      6R2
                      0     1      1     175


                      1 0          1      50
To make a32       0, 0 1         2       650        R3     R2     R3
                     0 0         3       825


                     1 0 0 225
                                                         1
To make a13      0, 0 1 2 650                  R1          R3   R1
                                                         3
                    0 0 3 825


                    1 0 0 225
                                                         1
To make a33      1, 0 1 2 650                  R3          R3
                                                         3
                    0 0 1 275


                      1 0 0 225
To make a23      0, 0 1 0 100                  R2         2R3     R2
                    0 0 1 275




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