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# sol3 - EE 221 Linear Systems HW#3 Solutions Sam Burden 1...

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EE 221 : Linear Systems HW #3 Solutions — Sam Burden — Sep 28, 2010 1 Note these solutions are overly terse and leave out some details; in your solutions, you should strive for greater clarity and rigor. Exercise 1. A E = 2 0 0 - 1 0 4 0 0 2 , A B = B - 1 A E B = 1 15 16 - 4 12 7 32 - 6 21 6 12 , B = 1 2 0 0 0 5 2 1 1 . Exercise 2. | x | = max j | x j | = q max j x 2 j s X j x 2 j = | x | 2 q n max j x 2 j = n max j | x j | = n | x | . Exercise 3. Consider a matrix representation A , apply the induced or 1 norm, and deduce |A| < by equivalence of norms on ﬁnite-dimensional vector spaces. Then observe ε > 0 : δ = ε |A| = ( | x - y | U < δ = ⇒ |A x - A y | V ≤ |A|| x - y | U < ε ) as desired . Exercise 4. These calculations are over C ; if you performed calculations over R , you should have made the assumption explicit! | A | = sup | u |
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