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+====== Math 445 HW3 solutions ======
+<code>
+John Gibson
+Math 445
+HW3 solutions
+Oct 7, 2014
+Problem 1: Given the vectors x=[3 7 2 9 0] and y=[7 10 2 8 13], what
+would be the Matlab output for the following expressions? Think
+through what the answer should be, write it down, and then try it out
+in Matlab. If you got anything wrong, figure out what your mistake was
+and why Matlab gave the answer it did.
+(a) x > y
+    [0 0 0 1 0]
+(b) y < x
+    [0 0 0 1 0]
+(c) x == y
+    [0 0 1 0 0]
+(d) x <= y
+    [1 1 1 0 1]
+(e) y >= x
+    [1 1 1 0 1]
+(f) x & y
+    [1 1 1 1 0]
+(g) x & (~y)
+    [0 0 0 0 0]
+(h) (~x) & (y)
+    [0 0 0 0 1]
+(i) x | y
+    [1 1 1 1 1]
+(j) xor(x,y)
+    [0 0 0 0 1]
+(k) (x > y) & (y < x)
+    [0 0 0 1 0]
+Problem 2: Write down Matlab expressions for the following. You can
+assume that a,b,c are logical variables, x,y,z are double-precision
+numbers, u,v,w are vectors of the same dimension, and A,B,C are
+matrices of compatible sizes.
+(a) Both a and b are true.
+    a && b
+(b) Neither a nor b is true.
+    ~a && ~b
+(c) Either a and b are both true, or b and c are both false.
+    (a && b) || (~b && ~c)
+(d) Either x equals y, or x is not equal to z.
+    (x == y) || (x ~= z)
+(e) x, y, and z are all equal.
+    (x == y) &&  (x == z) && (y == z)
+(f) None of the components of u equal the corresponding components of v.
+    ~any(u == v)
+(g) Each component of u is the same as either the same component of v or w.
+    all(u == v)
+(h) The vector whose components are the polynomial 3u^2 - 5u + 6 evaluated
+at each of the components of u.
+*u.^2 - 5*u + 6
+(i) The matrix product AB.
+    A*B
+(j) The matrix whose elements are the product of the elements of A and B.
+    A.*B
+Problem 3: A theater has a seating capacity of 900 and charges $2.50
+for children, $4 for students, and $5.50 for adults. At a certain
+screening with full attendance, there were half as many adults as
+children and students combined. The total money brought in was
+$3825. How many children, students, and adults attended the show?
+show?
+The equations are
+      c +  s +    a = 900
+.5c + 4s + 5.5a = 3825
+.5(c + s) = a
+or
+      c +    s +    a = 900
+.5c +   4s + 5.5a = 3825
+.5c + 0.5s -    a  = 0
+To put this in matrix-vector notation, let the column vector x
+have components [c  s  a]'. Then
+A = [1 1 1; 2.5 4 5.5; 0.5 0.5 -1];
+b = [900 3825 0]';
+x = A\b
+x =
+So 150 children, 450 students, and 300 adults attended the show.
+</code>

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