s01_ps04_fall03

s01_ps04_fall03 - Uniﬁed Engineering I Fall 2003 Problem...

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Unformatted text preview: Uniﬁed Engineering I Fall 2003 Problem S1 (Signals and Systems) 1. Consider the system of equations x + y − 2z = −1 x + 4y + 2z = 5 x + y − z = 0 Solve for x, y , and z , in three separate ways. The goal of part (1) is to practice solving systems of equations, so that when you get to part (2), you will have a fair basis of comparison. (a) Determine x, y , and z using (symbolic) elimination of variables. (b) Determine x, y , and z by Gaussian reduction. (c) Determine x, y , and z using Cramer’s rule. 2. Consider the system of equations 4x + 2y + 2z = 7 3x + y + 2z = 5 x + 3y − z = 4 Again, solve for x, y , and z , in three separate ways. This time, please time each part (a), (b), (c) below. (a) Determine x, y , and z using (symbolic) elimination of variables. (b) Determine x, y , and z by Gaussian reduction. (c) Determine x, y , and z using Cramer’s rule. (d) How much time did each method take? (e) Which method do you prefer? When answering this question, think about how much time might be required for a larger system, say, one that is 5 × 5. ...
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