Su96ex2 - Name ________________ SHOW ALL WORK! Problem 3...

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SU 96 EGN 3420 Exam 2 Name ________________ SHOW ALL WORK! Problem 1 (25 pts) For the system of equations x 3 + x 4 + x 5 = 2 3x 1 + 3x 2 - 2x 3 + x 4 + x 5 = 2 5x 1 + 3x 2 - 2x 3 + 3x 4 + x 5 = 4 x 1 + 2x 2 + x 3 + 2x 4 + 3x 5 = 5 A) Find the Echelon matrix and determine if the equations are consistent. B) If the equations are consistent, how many arbitrary unknowns are there? C) Can x 1 and x 2 both be arbitrary? If they can, use the Gauss Jordan method applied to the system of equations with x 1 and x 2 on the right hand side to find x 3 , x 4 , and x 5 in terms of x 1 and x 2 . ……………………………………………………………………………………………… Work Area
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SU 96 EGN 3420 Exam 2 Name ________________ SHOW ALL WORK! Problem 2 (25 pts) Find the value(s) of K for which the system of equations below does not possess a unique solution. w + x + y + z = 6 w + x + y - z = 0 2w - x + y = 1 w - 2x + Ky + 3z = 7 …………………………………………………………………………………………… Work Area
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SU 96 EGN 3420 Exam 2
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Unformatted text preview: Name ________________ SHOW ALL WORK! Problem 3 (25 pts) Solve the system of equations below using the Gauss-Seidel method. Start with an initial guess of x o = 1, y o = 1, z o = 1. Stop when the magnitude of the true error in z falls below 0.1, i.e. 3 - z i < 0.1 4x-2y + z = 3 x + 3y-z = 4 x-y + 4z = 11 Keep all intermediate calculations in terms of fractions. SU 96 EGN 3420 Exam 2 Name ________________ SHOW ALL WORK! Problem 4 (25 pts) Using Simpsons 1/3 Rule to approximate 1 1 1 I dx x = + The interval (0,1) is to be divided into 10 equal subintervals producing a step size of h = 0.1 Work Area i x i f i = f(x i ) 0.0 1.0000 1 0.1 2 0.2 3 0.3 4 0.4 5 0.5 6 0.6 7 0.7 8 0.8 9 0.9 10 1.0 0.5000...
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Su96ex2 - Name ________________ SHOW ALL WORK! Problem 3...

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