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gibson:teaching:fall-2014:math445:hw3solns [2014/10/07 10:43] (current)
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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.
 +    3*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
 +   2.5c + 4s + 5.5a = 3825
 +   0.5(c + s) = a
 +
 +or
 +
 +      c +    s +    a = 900
 +   2.5c +   4s + 5.5a = 3825
 +   0.5c + 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 = 
 +  150
 +  450
 +  300
 +
 +So 150 children, 450 students, and 300 adults attended the show. 
 +</​code>​
gibson/teaching/fall-2014/math445/hw3solns.txt ยท Last modified: 2014/10/07 10:43 by gibson