MATLAB HW5

MATLAB HW5 - Section B05 Nicholas Nguyen 5.1 a) > v =

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Section B05 Nicholas Nguyen 5.1 a) >> v = [2;0;-1];w=[1;3;3];x=[6;1;-3];y=[1;0;2];z=[2;-15;-1]; >> y'*x ans = 0 >> y'*z ans = 0 >> x'*z ans = 0 So the set {x, y, z} are all orthogonal to each other. The maximum number of non-zero orthogonal vectors that I can find in R 3 is 3, each of the x, y, and z axis are examples of 3 orthogonal vectors in R 3 . In R n , there can be n nonzero orthogonal vectors for each of the axis. Other sets include: {x,y} {x,w} {v,y} b) >> x = x/norm(x) x = 0.8847 0.1474 -0.4423 >> y = y/norm(y) y = 0.4472 0 0.8944 >> z = z/norm(z) z =
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0.1319 -0.9891 -0.0659 >> W=[x y z] W = 0.8847 0.4472 0.1319 0.1474 0 -0.9891 -0.4423 0.8944 -0.0659 5.2 a) >> W'*W ans = 1.0000 0 0 0 1.0000 0 0 0 1.0000 We get this because the transpose of an orthogonal matrix is the same as its inverse. Therefore any inverse times the original matrix give you the identity matrix. b) >> a =[1;1;0]; b=[2;0;3]; >> b = b/norm(b) b = 0.5547 0 0.8321 >> c=W*b c = 0.6004 -0.7412 -0.3002 >> c = c/norm(c) c = 0.6004 -0.7412 -0.3002
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This note was uploaded on 03/20/2012 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.

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MATLAB HW5 - Section B05 Nicholas Nguyen 5.1 a) > v =

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