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**Unformatted text preview: **MATH 129A Linear Algebra I Project 1 Due in class on 2/17/2010 (W) There are many applications of systems of linear equations. Well over 75 percent of all mathe- matical problems encountered in scientific or industrial applications involve solving a linear system at some stage. The important thing is to recognize that a problem can be formulated as a linear system, and the answer can be obtained by solving the linear system. Below are four examples to test your ability in doing so. 1. A Babylonian clay tablet that survives from about 300 B.C. contains the following problem: There are two fields whose total area is 5349 square yards. One field produces grain at the rate of 3 4 bushel per square yard; the other field produces grain at the rate of 2 3 bushel per square yard. If the total yield is 3733 bushels, what is the size of each field? (a) Define the two unknowns x 1 and x 2 . (b) Write down the system of two linear equations in x 1 and x 2 ....

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