acteria II, and bacteria III. In the test dish, these three types of bacteria were given three types of food, namely food A, food B, and food C. Every day 1600 units of food A,3000 units of food B, and 4500 units of food C were placed in the test dish and each type bacteria consume a number of food units as shown in the following table: Bacteria I Bacteria II Bacteria III Food A 1 1 2 Food B 1 2 3 Food C 1 3 5 (1) If we denote x1 for bacteria I, x2 for bacteria II, and x3 for bacteria III. Write a system of linear equations for each type of food.
A bacterial researcher is conducting an experiment by collecting three types (strains) of bacteria in a test dish. Each type of bacteria is coded for bacteria I, bacteria II, and bacteria III. In the test dish, these three types of bacteria were given three types of food, namely food A, food B, and food C. Every day 1600 units of food A,3000 units of food B, and 4500 units of food C were placed in the test dish and each type bacteria consume a number of food units as shown in the following table:
| Bacteria I | Bacteria II | Bacteria III | |
| Food A | 1 | 1 | 2 |
| Food B | 1 | 2 | 3 |
| Food C | 1 | 3 | 5 |
(1) If we denote x1 for bacteria I, x2 for bacteria II, and x3 for bacteria III. Write a system of linear equations for each type of food.
(2) Make a system of linear equations number (1) in the form of matrix and
(3) Calculate the determinant of matrix A using the row reduction method
(4) Find x1, x2 , and x3, using Cramer's rule, so that the bacterial researcher knows how many bacteria per type (or strain) must be put in the test dish so that all the food provided is eaten.
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