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# Test1B - PGE 310 TEST#1 1 Short Answer SHOW ALL WORK(60...

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PGE 310 TEST #1 (Sept 30, 2009) 1. Short Answer. SHOW ALL WORK (60 points total; 6 pts each except (h)) Consider the following arrays for (a), (b), and (c) only u=[2 -3 2]; v=[ 3 2 0]; A=[1 -1; 2 3; -1 3]; B=[ 2 1; 2 3] (a) Compute by hand >> A(:,2)’*u >> A(:,2)’*u Let z= A(:,2) = 1 3 3 -           z’= [1 1 2] z’*u is not possible as both are row vectors (b) Compute by hand >> B*B >> B*B = 2*2 1*2 2*1 1*3 2*2 3*2 2*1 3*3 + + + + B*B = 6 5 10 11 (c) 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 .... ) ( 2 3 2 ) 17 L norm of u is u u u = + + = + - + = 2 2 2 1/2 2 2 2 1/2 2 ( 1 2 3 .... ) ( 3 2 0 ) 13 L norm of v is v v v = + + = + + =

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In order to find the orthonormal vector, divide the given vector by its L2 norm ^ 2 u u L norm of u = Thus, ^ [2 3 2] 13 u - = ^ 3 1 * 2 17 0 v     =       (d) Write the MATLAB code that is equivalent to the following : ( ) 100 50 2 2,4,6 1 5 2 j k j k = = + + ∑ ∑ sum=0; for j=2:2:100 for k=1:50 sum=sum+(j*j+5*k+2); end
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Test1B - PGE 310 TEST#1 1 Short Answer SHOW ALL WORK(60...

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