% Diary file from Matlab for hw1.

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%  Problem 2:

A=[10 -3; 4 2], B=[1 0; -1 2], v=[1; 2], w=[1; 1]

A =

    10    -3
     4     2


B =

     1     0
    -1     2


v =

     1
     2


w =

     1
     1

%   2(a):
v'*w

ans =

     3

%   2(b):
v*w'

ans =

     1     1
     2     2

%   2(e):
A*B

ans =

    13    -6
     2     4

%   2(f)
B*A

ans =

    10    -3
    -2     7

%   2(h)
y=B\w

y =

     1
     1

%   2(i)
x=A\v

x =

    0.2500
    0.5000
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%  Problem 3:

x=[0:.01:2*pi]';
for k=1:5, y=sin(k*x); plot(x,y), hold on; end;
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%  Problem 6:

figure(2)    % Put plot on a new graph.
subplot(2,2,1)  % Use subplot to put 4 graphs on same page.
x=[-3:.01:3]'; y = abs(x-1); plot(x,y); title('y = abs(x-1)')
subplot(2,2,2)
x=[-4:.01:4]'; y=sqrt(abs(x)); plot(x,y); title('y = sqrt(abs(x))')
subplot(2,2,3)
x=[-4:.01:4]'; y=exp(-x.^2); plot(x,y); title('y = exp(-x^2)')
subplot(2,2,4)
x=[-2:.01:2]'; y=1./(10*x.^2+1); plot(x,y); title('y = 1/(10 x^2 + 1)')
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%  Problem 11:

figure(3)   % Put plot on a new graph.

%   11(a):
%   Create matrix whose columns contain coords of each vertex of the square.
U = [1 2 2 1; -.5 -.5 .5 .5];
%   Plot a red square.
fill(U(1,:),U(2,:),'r')
%   Adjust axes.
axis('equal'); axis([-4 4 -4 4]); hold on

%   Create rotation matrix.
theta = pi/4;
R = [cos(theta), -sin(theta); sin(theta), cos(theta)];
% Rotate each of the vertices and color the rotated square blue.
U = R*U;
fill(U(1,:),U(2,:),'b')

%   Continue rotating, coloring rotated squares different colors.
U = R*U;
fill(U(1,:),U(2,:),'g')
U = R*U;
fill(U(1,:),U(2,:),'y')
U = R*U;
fill(U(1,:),U(2,:),'m')
U = R*U;
fill(U(1,:),U(2,:),'c')
U = R*U;
fill(U(1,:),U(2,:),'r')
U = R*U;
fill(U(1,:),U(2,:),'b')
U = R*U;
fill(U(1,:),U(2,:),'g')  % This square lands on top of original.

%  11(b):
figure(4)  % Put next plot on a new graph.
U=[5 6 4; 0 2 1];
fill(U(1,:),U(2,:),'r')  % Plot initial red triangle.
hold on                  % Put next plot on same graph.
theta = pi/2;
R = [cos(theta), -sin(theta); sin(theta), cos(theta)];
U = R*U;                 % Rotate pi/2 radians.
fill(U(1,:),U(2,:),'b')  % Plot rotated triangle in blue.
U = R*U;   % Rotate another pi/2 radians for a total of pi.
fill(U(1,:),U(2,:),'g')  % Plot rotated triangle in green.
U = R*U;   % Rotate another pi/2 radians for a total of 3*pi/2.
fill(U(1,:),U(2,:),'y')  % Plot rotated triangle in yellow.
axis('equal')

%   11(c):
%   Verify that R(theta) and R(-theta) are inverses of each other
%   for theta=pi/3 and theta=pi/4.
theta=pi/3;
Rtheta = [cos(theta), -sin(theta); sin(theta), cos(theta)];
Rmtheta = [cos(-theta), -sin(-theta); sin(-theta), cos(-theta)];
Rtheta*Rmtheta

ans =

     1     0
     0     1

% This is the identity, so Rtheta and Rmtheta are inverses of each other.

theta = pi/4;
Rtheta = [cos(theta), -sin(theta); sin(theta), cos(theta)];
Rmtheta = [cos(-theta), -sin(-theta); sin(-theta), cos(-theta)];
Rtheta*Rmtheta

ans =

     1     0
     0     1

% This is the identity, so Rtheta and Rmtheta are inverses of each other.
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exit