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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 Fall '05
 MarkDrela
 Linear Algebra, Equations, Elementary algebra

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