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# Su97ex2 - 1 1 1 2 2-1-3-3 1 1-2 3-3-3-1 1 1-1-1 1 3 1 5-2-2...

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Su 97 EGN 3420 Exam 2 Name___________________ SHOW ALL WORK! Problem 1 (20 pts) Solve the following system of equations using the Gauss Jordan Elimination Method. a + b + c + d = 0 2a - b - c + d = 3 a + 3b + 2c - 4d = -1 5a + 2b - 2c + d = 7 ......................................................................................................... Work Area (A|b ) = 1 1 1 1 2 1 1 1 1 3 2 4 5 2 2 1 0 3 1 7 - - - - -

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Su 97 EGN 3420 Exam 2 Name___________________ SHOW ALL WORK! Problem 2 (25 pts) Consider the following system of equations: u + v + w = 2 2u - v - 3x - 3y = 1 u - 2v + 3w - 3x - 3y = -1 u + w - x - y = 1 3u + v + 5w - 2x - 2y = 4 A) Show the equations are consistent by transforming the augmented matrix (A|b ) into its Echelon Form by performing a sequence of elementary row operations. B) There are 2 arbitrary unknowns. Explain why. C) Without solving for a solution determine if x and y are both arbitrary. D) Repeat Part C) for x and w. E) What conclusion can be drawn from the results of Part C) and D)?

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Unformatted text preview: 1 1 1 2 2-1-3-3 1 1-2 3-3-3-1 1 1-1-1 1 3 1 5-2-2 4 Augmented Matrix Su 97 EGN 3420 Exam 2 Name___________________ SHOW ALL WORK! Problem 3 (25 pts) Find the value(s) of K in the system of equations below which result in an infinite number of solutions. Use only methods discussed in class. x 1 + 4x 2 + 7x 3 =-5 x 1 + x 2 + x 3 = 1 2x 1 + 3x 2 + 4x 3 = x 1-x 2 + Kx 3 = Su 97 EGN 3420 Exam 2 Name___________________ SHOW ALL WORK! Problem 4 (30 pts) Consider the system of equations Ax =b below. 1. Find the inverse of A and the solution x =A-1 b . 2. Perform two iterations of the Gauss-Seidel method and compute the true errors in x, y and z, i.e. (E T ) x , (E T ) y and (E T ) z at the end of the second iteration. Start with an initial guess of x = y = z = 1. 5x + y + z = 45 x + 5y + z = 25-x + y + 5z =-55...
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