Test1A - TEST#1 PGE 310 1 Short Answer SHOW ALL WORK(60...

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TEST #1 (Sept 30, 2009) PGE 310 1. Short Answer. SHOW ALL WORK (60 points; 6 pts each except (h)) Consider the following arrays for (a), (b), and (c) only u=[1 -2 1]; v=[ 3 1 -1]; A=[2 1; 3 1; -2 2]; B=[ 1 2; 3 1] (a) Determine if u and v’ are orthogonal. If they are, make them orthonormal with respect to the L 2 norm. u.v’ = 0 Hence they are orthogonal. 2 2 2 1/2 2 2 2 1/2 2 ( 1 2 3 .... ) (1 2 1 ) 6 L norm of u is u u u = + + = + - + = 2 2 2 1/2 2 2 2 1/2 2 ( 1 2 3 .... ) ( 3 1 1 ) 11 L norm of v is v v v = + + = + + - = In order to find the orthonormal vector, divide the given vector by its L2 norm ^ 2 u u L norm of u = Thus, ^ [1 2 1] 6 u - = ^ 3 1 * 1 11 1 v = - (b) Compute by hand >> A(:,2)’*u Let z= A(:,2) = 1 1 2           z’= [1 1 2] z’*u is not possible as both are row vectors (c) Compute by hand >> B*B

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= 1*1 3*2 1*2 2*1 3*1 3*1 3*2 1*1 + + + + B*B = 7 4 6 7 (d) The pressure in a system is a function of both temperature and concentration. It is governed by the following equation. ( )
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Test1A - TEST#1 PGE 310 1 Short Answer SHOW ALL WORK(60...

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