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MAT183-2007Spring - MAT 183 Spring 2007 YY F inal Exam A 5...

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MAT 183 - Spring 2007 Final Exam YY\ A !5 \ 1':)& 1 LA Name: __________________ __ Signature: _____________ _ Instructions: Show all the work you want graded on this exam. Unsupported answers may receive little or no credit. List the values you put into your calculator. Problem Points Score 1 6 2 6 3 5 4 6 5 5 6 6 7 6 8 5 9 6 Total 51 Part I: Linear Algebra 1. a. (2 pts) Find the sum of the matrices. P -6 1-2 4 ~2 7 + 18 -5 b. (4 pts) Suppose a and b are constants and the inverse of the matrix ax + by + 3z == 7 Use this to find the solution to the following system of equations: x + y + 5z == 2 { 2x+ y+9z =3 1
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2. Each of the following matrices is the matrix of a system of linear equations in x, y and z. Find all solutions to the system of equations in each case. 2 -1 0 2 2 a. (3 pts) 0 1 b. (3 pis) ~ 1 1 4 4 -2 1 5 9 ~ ~ 3. (5 pts) A business has a plastics division and a metal division. For each $1 worth of output, the plastics division needs 10¢ of output from the plastics division and 6¢ from the metal division. For each $1 worth of output, the metal division needs 12¢ of output from the plastics division and 14¢ from the metal division. What level
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