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# Sp95ex2A - C If the equations are consistent and there are...

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Sp 95 EGN 3420 Exam 2A Name___________________ SHOW ALL WORK Problem 1 (40 pts) Consider the following system of equations: x 1 + x 2 + x 3 - 2x 4 + 2x 5 = 1 2x 1 - x 2 + 3x 3 - 2x 4 + 2x 5 = 3 3x 1 - 4x 3 + 4x 4 - 4x 5 = -4 4x 1 - 3x 2 + 3x 4 - 3x 5 = 0 x 1 + 3x 3 - 3x 4 + 3x 5 = 3 A) Transform the augmented matrix into Echelon Form. ( 29 A b = - - - - - - - - - 1 1 1 2 2 2 1 3 2 2 3 0 4 4 4 4 3 0 3 3 1 0 3 3 3 1 3 4 0 3 Which of the following statements are true? The equations are inconsistent. The equations are consistent and there is a unique solution. The equations are consistent and there is 1 arbitrary unknown. The equations are consistent and there are 2 arbitrary unknowns.

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B) If the equations are consistent and there is a unique solution, find it. If the equations are consistent and there is 1 arbitrary unknown, determine if x 1 can be arbitrary without solving for it . If the equations are consistent and there are 2 arbitrary unknowns, determine if x 1 can be one of the arbitrary unknowns without solving for it

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Unformatted text preview: . C) If the equations are consistent and there are one or more arbitrary unknowns, express the solution in terms of the arbitrary unknown(s). Sp 95 EGN 3420 Exam 2A Name___________________ SHOW ALL WORK! Problem 2 (30 pts) Find the equation of the Least Squares line which best fits the quadratic y = x 2 + 1 over the interval (0,5). Do this by generating 6 equally spaced points over the interval (0,5) from the quadratic. i x i y i = x i 2 + 1 1 1.0000 2 1 3 2 4 3 5 4 6 5 Sp 95 EGN 3420 Exam 2A Name___________________ SHOW ALL WORK! Problem 3 (30 pts) Consider the definite integral 1 2 x I e dx-= ∫ . A) Use Trapezoidal integration with n=5 intervals to approximate I. B) Find the truncation error. Round all calculations to 5 places after the decimal point. i i x 2 i x i f e-= 1 2 3 4 5...
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Sp95ex2A - C If the equations are consistent and there are...

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