Test1B - PGE 310 TEST #1 (Sept 30, 2009) 1. Short Answer....

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 = + + = + + =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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;
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/19/2012 for the course PGE 310 taught by Professor Klaus during the Spring '06 term at University of Texas at Austin.

Page1 / 6

Test1B - PGE 310 TEST #1 (Sept 30, 2009) 1. Short Answer....

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online