hw2soln_f09

hw2soln_f09 - ME 132 Fall 2009 Solutions to Homework 2 1. (...

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Unformatted text preview: ME 132 Fall 2009 Solutions to Homework 2 1. ( § 1.3 Problem 2) This problem can be solved by getting rid of intermediate variables by plugging the three equations into each other. For example, if you want to express y as a function of r , d , and n , start with the given equation for y and plug in for the variables you don’t want: y = Pu + Pd = PCe + Pd = PC ( r- y- n ) + Pd = PCr- PCn + Pd- PCy ⇒ (1 + PC ) y = PCr- PCn + Pd y = PC 1 + PC r- PC 1 + PC n + P 1 + PC d The other equations are: e = 1 1 + PC r- 1 1 + PC n- P 1 + PC d u = C 1 + PC r- C 1 + PC n- PC 1 + PC d These equations may be expressed in matrix form since they are linear in r , d , and n . e u y = 1 1+ PC- 1 1+ PC- P 1+ PC C 1+ PC- C 1+ PC- PC 1+ PC PC 1+ PC- PC 1+ PC P 1+ PC r n d = 1 1 + PC 1- 1- P C- C- PC PC- PC P r n d 2. ( § 1.3 Problem 6) (a) (b) A, B ∈ C . i. Derive | AB | = | A || B | Recall that AB = ( A R + jA I )( B R + jB I ) = ( A R B R- A I B I ) + j ( A I B R + B I A R ) So | AB | = bracketleftbig ( A R B R- A I B I ) 2 + ( A I B R + A R B I ) 2 bracketrightbig...
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This note was uploaded on 10/20/2010 for the course ME 132 taught by Professor Tomizuka during the Spring '08 term at Berkeley.

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hw2soln_f09 - ME 132 Fall 2009 Solutions to Homework 2 1. (...

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